Let me clarify. I do not consider anyone who attends the indult to be a 'traditional' catholic. They are duped and/or have compromised their faith. So, when i say 'traditional' catholic, I mean only those who EXCLUSIVELY attend a sedevecantist, sspx, or independent chapel.
I am assuming that 99% of traditional catholics already know that rome has lost the faith, already know that V2 is wrong, etc. Otherwise, they wouldn't be a 'trad'. So, if all 'traditional' catholics went 'sede' tomorrow, what would you hope would change?
I'm trying to understand why this issue matters, in a practical sense. Both the sspx and the 'sede' camps argue about this incessently, yet I do not get the urgency, other than for competition and for 'their side' to win.
Thank you for this awesome and well-stated question which is an incredibly good question to ask.
Please know that while your general assumption is correct, that some actually do find themselves attending SSPX chapels merely because they like the Mass they offer while not realizing that they are "schismatic". I know an individual where this was the case and figure she was not the only one.
I do not speak to you but generally state that the idea that the Pope issue is not important or secondary is false. Speaking in such terms during the reign of Pius XII would be considered to be absurd. The rock upon which the Church is built is about as important as it gets. So to is his legitimacy whether he be a valid Pope who would be leading souls to Heaven or a false Pope who is leading souls to Hell and preventing conversions due to the fact that any sincere protestant that follows the man knows that his religion can't be true and his religion, so they suppose, is the Catholic religion.
I remember about nine years ago when I received something in the mail from the SSPX where in it they stated matter-of-factly that the traditional Mass is the "extraordinary" form of the liturgy. I was SV at the time but I had respect for the SSPX until that time. They had gotten significantly worse in the short time-frame of a few years that I followed them somewhat. Why was this? Because Father Ratzinger, their new Pope, was their last great hope for "making the Catholic Church Catholic again" as if such a thing would ever be necessary. My point is you have to be rooted in truth without compromise in order to have the truth without compromise. Insisting that a public heretic is the head of the Roman Catholic Church leads to a skewed theology that can be damning. This is more of a side note than a direct response to your question.
The answers to your question are as follows:
1. The credibility of the New Church would suffer tremendously if all "trads" were sedevacantist because then the Vatican II Sect could not so easily claim to be the Catholic Church, if there are millions out there who are as Catholic as Pius XII but don't recognize the bozos in Rome as actual Catholics.
2. The whole strength of the revolution lies in the idea that the people who have been perpetrating it are Catholic authorities. Raising awareness that they are not is essential, also with regard to a testimony to non-Catholics, secularists, etc., that what is going on there in Rome is a new religion.
3. The practical consequences are not nearly as important as the fact that we have an obligation in justice to do what is right and affirm what is true and reject what is false, regardless of whether that accomplishes anything in practice or not. We are obliged to know the truth and act accordingly. The results, ultimately and inevitably, will be good - the salvation of more souls, through converts and properly formed Catholics.
4. To approach this from a perspective of, "How will this change anything for the Vatican II Church?", is wrong. The question can be asked, of course, but it can't be the primary concern. The SSPX position does great harm to Catholic teaching. That alone is sufficient reason to abandon it. You cannot wipe that away by saying "well but they too reject Vatican II". So? Rejecting Vatican II for the wrong reason isn't good enough. If someone argues that Francis is not the Pope because he wears glasses, then I can't say, "Hey, at least he's rejecting Francis, so what does the rest matter!" No, it matters a LOT.
I hope this helps some. The bottom line is the truth matters in all things but especially in regards to the Papacy and whether its claimants are valid or not as can be attested to Christ going to the trouble of building the whole thing upon it.