You have never witnessed the "forbidden fruit" syndrome?  It's very common when kids go to college.  They get their first taste of freedom and then go crazy in overdoing all manner of vices.  Kids whose parents do not allow them to consume alcohol, for instance, are generally the most likely to be found throwing up every night / morning in the dorms.  For those who have had a little here and there, well, alcohol has less of an allure for them.

I will not list names, but I would say that the majority of Traditional Catholic children in the two chapels near me have gone off the deep end after becoming independent.  Several marriages in the Novus Ordo, much sinful cohabitation (sometimes with the fiction of a civil marriage).  Many of these are now divorced.  Quite a few have ceased practicing the Faith altogether.  And, from what I have seen, the more strict their parents were when they were growing up, the farther they strayed.  Young men and women who are ultimately called to the married state often become frustrated with the lack of suitable prospects at their relatively-small chapel populations.  So, often, the second they find someone to whom they are attracted, they go for it.  Very, very common.  I think it's healthy for youngsters to mingle in controlled public settings (no exclusive dating) with members of the opposite sex.  That way they can develop a sense for the type of person they would be compatible with, and the allure/mystique of the opposite sex quickly wears thin.

  And, from what I have seen, the more strict their parents were when they were growing up, the farther they strayed. 

What is strict?

Interestingly, I had a long conversation with a friend the other day about this very question.  My children are very young but this is something I certainly wonder about.
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I myself was definitely a victim-- or participant might be a better way to put it-- in the forbidden fruit syndrome.  So I ask myself, "what could my parents have done differently so that I cared about religion from ages ~12-20?"  Latin mass only attendance, rosary every night, all the sacraments on time, etc. obviously wasn't enough.  And it's not like kids don't have free will; theoretically everything could be done right and the kid could still be lost.  Think of the prodigal son (who of course eventually returned, but the point is that he was lost for quite a while).  So maybe they did do everything they could have.  But if it's a widespread phenomenon, then my guess is that there's something more the parents could do.
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I don't exactly know the answer to that, but something my friend and I think might play a role is not just a "lack of catechetics" but a lack of philosophical formation in particular.  When kids are preparing for Holy Communion, they're taught the catechism as a recitation.  But at a certain point a child, perhaps even without explicitly realizing it, will ask himself why he believes what he does (asking this question is, IMO, good).  And at a certain point "because my parents told me" is simply not a sufficient reason.  What's left?  No amount of recitation will communicate the underlying reasons, IMO.  Recitation is good for learning the basics, and it's good in prayer for reinforcing virtue through practice.  After that it's utility is questionable.
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If, on the other hand, a kid has a strong philosophical foundation-- he doesn't just know the basics of the faith but he knows why they're true, especially the ones that can be demonstrated a priori (like God's existence) or with enormous historical credibility (the formation and existence of the Catholic Church, the fact of the Resurrection, etc.), I have to imagine it'd be much harder to throw away.  Because it's not like the kid is going to approach his parents who've only ever just had him recite (however frequently) the Baltimore Catechism about some concern or another.  No, if he starts to question he's very probably going to keep it to himself and slowly defect (which was my own trajectory).  Combine that intellectual slide with the world, the flesh, and the devil and the end destination is a foregone conclusion.  When those temptations and questions come up, kids need something beyond "my parents told me."  They need something.  This is not an imperfection of theirs, I think it's human nature.  We're rational animals.  When we become men, we put aside the things of children.  Part of that means understanding the world (metaphysically) independently from what you were told as a child. 
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Grace builds on nature.  If you never know why you believe what you do and you're exposed to the temptations and arguments of the world, don't expect your faith to stick around for very long.  I think kids probably need to receive a fuller, stronger foundation in the supporting elements of the faith.  This keeps things interesting, engaging, and most importantly it helps them form critical thinking skills and also progressively shows them that we can submit the Catholic faith to virtually any and every challenge and the Catholic faith will win.  I'm sure there's a strategic balance to be struck as well-- you probably don't want to sit down with an eight year old and say "let's see if we can prove God doesn't exist"-- but with a thirteen year old?  Maybe!  I don't have a perfect strategy developed for this, and I'm sure it would vary from family to family, from child to child.
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I'll close by pointing out that this is especially important now.  It wouldn't be as important in a Catholic society, because you would have the useful social controls and pressures to at least nominally reinforce standards of Catholic behavior.  So you could "get away" with, at least at face value, a shallower catechetics since your kids are going to be marrying other Catholics and continuing to go to mass and practice the faith no matter what-- they pretty much don't have a choice unless they really want to break off and go join the Caliphate or something.  But no such society exists now, so there needs to be a strong, commensurate reason to stay Catholic since there won't be any serious social consequences for not remaining in the Church.

You have never witnessed the "forbidden fruit" syndrome?  It's very common when kids go to college.  They get their first taste of freedom and then go crazy in overdoing all manner of vices.  Kids whose parents do not allow them to consume alcohol, for instance, are generally the most likely to be found throwing up every night / morning in the dorms.  For those who have had a little here and there, well, alcohol has less of an allure for them.

I will not list names, but I would say that the majority of Traditional Catholic children in the two chapels near me have gone off the deep end after becoming independent.  Several marriages in the Novus Ordo, much sinful cohabitation (sometimes with the fiction of a civil marriage).  Many of these are now divorced.  Quite a few have ceased practicing the Faith altogether.  And, from what I have seen, the more strict their parents were when they were growing up, the farther they strayed.  Young men and women who are ultimately called to the married state often become frustrated with the lack of suitable prospects at their relatively-small chapel populations.  So, often, the second they find someone to whom they are attracted, they go for it.  Very, very common.  I think it's healthy for youngsters to mingle in controlled public settings (no exclusive dating) with members of the opposite sex.  That way they can develop a sense for the type of person they would be compatible with, and the allure/mystique of the opposite sex quickly wears thin.

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It's a little bit like the theory behind inoculation.  The theory behind inoculation is good and sound, and pretty much everyone practices it.  The idea is that at some points in life your immune system is weak, at other times, it is strong.  When it's weak (e.g. a newborn) you limit exposure to any and all possibilities of disease.  But then when your kid is five, you have a chicken pox party.  They're stronger, they can "handle it," and it'll be much worse if they have to deal with it as adults.  There are of course some things you never expose them to, and you never just carelessly throw them into rooms with diseased people, but to the degree that they are so exposed and supervised through the difficulty, you see them develop an interior strength to help manage and respond to such forces.
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Similarly with morals, it seems that some exposure to the world-- whatever exactly that entails, is obviously up for debate-- is necessary in the interest of the formation of good morals.  

The way I’ve heard it explained is that a parent can’t be an authoritarian without having established a positive relationship with the child.  If there are rules in absence of love/acceptance, the child will look for love/acceptance other places, which the parent will see as “rebelling”.  The child won’t see it as rebelling, they’ll see it as escaping a dictator.  

But if the child knows he’s loved and has a relationship with his parents then he’ll trust the rules and be more open to following them.  

There's probably a lot to this, Pax.  As you said, sometimes it's about children seeking love/acceptance.  We all yearn for that naturally.  But sometimes, even when they do get this from their parents, they seek a more intimate type of love/acceptance from the opposite sex.

Let me give you a couple examples of my own personal development.

Initially I thought that I would never allow my girls to wear ANY makeup.  I considered it to be wanted by girls only for impure purposes.  I grew up with 3 brothers and was out of the house when my one young sister got older (she was 8 when I was gone).  And my mother never wore makeup ... not out of principle, but just because she never felt like it.  I have four daughters now, and both the older ones, when they hit puberty, developed acne (inherited through their Mom's side).  And I was shocked by the degree to which they were derided by their Traditional Catholic female friends.  They asked if they could wear some stuff to cover up, and of course I let them.  Nothing heavy, but just enough to make them feel not "repugnant".  Imagine if I had stuck to my guns, as some Traditional Catholic parents had done, and they spent years and years feeling "repulsive" to other people.  That would cause severe emotional and psychological scars for a girl.  So I came to the realization that there's nothing inherently wrong with a girl just wanting to feel pretty.  And I also realized that 99% of the time, it was in relation to their FEMALE peers, that they wanted to feel pretty, and not because they were trying to "ensnare" some boy.  So as long as I don't sense any impure motives, I let them wear some light makeup, just so they can feel pretty.  And I let them wear nice clothes (provided they're not in any way immodest) ... instead of imposing the "Little House on the Prairie" look that many Traditional Catholics require of their girls.

But sometimes, even when they do get this from their parents, they seek a more intimate type of love/acceptance from the opposite sex.

Yes, in this case it's more of a "black sheep" mentality or an adventurous spirit in the child (i.e. a choleric who likes to challenge the rules).  But...i've never seen a child who had a good relationship with their parents give up the faith totally.  Yes, they could make some horrible decisions and screw up their life immensely but they wouldn't give up religion (or at least not due to hostility.  They could give it up due to laziness or for pleasure, but that has nothing to do with the parents and this kind of reason can be overcome by grace - see St Mary Magadalen or St Augustine.  But when a person gives up religion due to hatred or "rational" reasons, only the grace of God can overcome this strong emotion).

On the contrary, i've seen some kids (some relatives) who had a bad relationship with their parents (both parent/child were to blame) but otherwise had a great childhood and they gave up religion even though they never did anything crazy or extremely stupid.  They were just "blah" towards the whole idea of God.  This, of course, was a gradual process, but their foundation for loving God was greatly compromised by their disfunctional family.  (Again, this was not all the parent's fault).

Then you have the case of the loving parents but who are strict, not in the sense of not allowing freedom, but who are just "control freaks" and don't know how to "let go" and let their children legitimately experience AND FAIL at life.  They don't know how to let a 13 year old decide when/how to do their homework and face the consequences at school (the parents continue to micro-manage the teenager just like they did when he was 3 or 4).  If parents don't let their kids make dumb decisions at a young age, they'll make them when they're out of the house at 18 or 20.  You can't avoid dumb decisions; you can't avoid life lessons.  Failure is the best teacher there is.  But you have to let them fail in a controlled environment or else they will fail when no one is around and the consequences are more extreme.

Then there are some kids just have to go wild to figure out the limits of life and experience first-hand the idiocy of their ways (i.e. Prodigal son, St Augustine, St Mary Magdalen, etc).