I've heard stories of missionaries baptizing natives in some pretty creative ways, and they (the North American Martyrs) became saints.
Were they exempt from asking permission because of their missionary status?

So who is really left in the lurch? It's really the poor unchurched child that follows the proscriptions of the NO and can't enter heaven if they die before the age of reason.

And the answer is always in God's providence.  There's a reason that God allows certain souls to be born among pagans and others to Catholic parents.

But the Church's teaching has always been that people should be properly prepared to receive the Sacrament.  As adults, that meant a sometimes-lengthy period of instruction and testing.  For infants, that happens vicariously through the parents and the intention/promise to provide such instruction as the child grows toward the age of reason.  It's the same difference.

We apply Catholic principles and leave the rest up to God.  We do not do theology based on emotion.

So what's the logical consequence?  If I'm a nurse who works the maternity ward, do I just go around randomly baptizing every infant?  This does grave harm to the Sacrament.  As a priest, do I go around shoving consecrated Hosts into people's mouths because of the graces they would receive from this ... regardless of whether the person might be a Catholic, in a state of grace, and properly disposed (fasting)?  The Church has always taught and held that people must be PROPERLY DISPOSED to receive the Sacraments; otherwise their reception would be sacrilege.  

Every prayer book states the proper way for a lay person to baptize in an emergency, yet NOT EVEN ONE states that you should ask the person if they want to be baptized.

That's simply assumed.  If the person is conscious, then they must indicate their desire to receive the Sacrament.  And the Holy Office stated that even in danger of death, the Sacrament could not be conferred without at least a basic minimal catechesis (of the four essential truths of the faith).  Then, even when a person falls unconscious, there must have been some PRIOR indication of the person's interest in becoming a Catholic.  Just ask any priest who has had courses in pastoral theology and not rely on an oversimplified "prayer book".

No of course you can't baptize every HEALTHY infant, no one is saying you should!  but what about a dying newborn? Would the baptism be valid? I would think it a sin not to baptize that baby. In many circuмstances every second counts. It's literally do or die. What are the consequences of NOT baptizing in those circuмstances? This puts a lot of pressure on the person trying to make that decision in a dire situation.What does properly disposed mean when facing the impending death of a child?

Also, why DOES the Church acknowledge the validity of baptisms from most other protestant sects when they know the person/ infant/parents are not properly disposed ?

Of course the baptism would be valid for a dying newborn, just the same as it would be valid for any healthy person - and yes, an infant whose death is certainly imminent, can be baptized by anyone and should be baptized without delay. Should that child live, the parents are responsible to raise the child a Catholic.

Regardless of whatever false religion it happens, all baptisms done properly are valid, but adults who receive it outside of the Church as if it is nothing more than a type of initiation, commit a sacrilege and are in sin immediately after they are baptized - because not only did they receive the sacrament with an improper disposition, they received it for the wrong reason altogether.

In a nutshell, for those baptized outside the Church, if they had known the Church's actual requirements for the reception of the sacrament, they would have never desired or wanted to be baptized at all.

The sacraments belong exclusively to the Church, the  Church is the *only* guardian and protector of the sacraments, as such, She makes the rules. You want Her sacrament? - then you must be Catholic, *that's* the foundational rule and it applies to all of the seven sacraments all of the time. 

No of course you can't baptize every HEALTHY infant, no one is saying you should!  but what about a dying newborn? Would the baptism be valid? I would think it a sin not to baptize that baby. In many circuмstances every second counts. It's literally do or die. What are the consequences of NOT baptizing in those circuмstances? This puts a lot of pressure on the person trying to make that decision in a dire situation.What does properly disposed mean when facing the impending death of a child?

Also, why DOES the Church acknowledge the validity of baptisms from most other protestant sects when they know the person/ infant/parents are not properly disposed ?

At no point did anyone say that these would not be valid.  Question is whether it would be licit or whether it would be a sin against the Sacrament.