Clarence's son was barred by attainder, and it would have taken an act of parliament to reverse I think, but yes, could have been done.
I think you have to see it in terms of pragmatic calculation about the stability of the polity (possibly to an extent driven by panic), and that probably would exclude allowing another minor, particularly one, as you say, "simple-minded", to succeed.
But if you accept that Richard was pragmatic in excluding Edward of Warwick from the succession, then I think you have to at least allow for the possibility that either he or his followers might have been "pragmatic" in other ways
. Like I say, the extinguishing of rivals and/or predecessors was not unknown in the medieval succession, even within families.
Incidentally, it's not clear to me that Richard's loyalty to Edward was anything other than pragmatic either. He didn't join the 1469 or 1470 rebellions, but then he wasn't being offered what Clarence was AFAIK. In fact, given that Edward found it extremely difficult to provide for both of them in terms of land, heiresses etc in the 1460s as they both came of age, the logical thing for Richard to do was simply to make sure he was on the opposite side to Clarence, whatever that was. Edward was really scratching around in the 1460s trying to provide for them both and failing because he had so many supporters to reward, and that's part of the reason why Clarence rebelled. If Richard stuck with Edward he was automatically booting himself up the list for preferment if Edward prevailed - and that's exactly what happened. Clarence backed the losing horse both times, tried it again later and paid the price.
Medieval noble families are very odd things. I just don't know enough about family relationships and social history, I was more high politics. But to me that family - with all its internal schisms, brother against brother, its rumours flying around for years about illegitimacy etc (Edward's as well as the princes') - looks dysfunctional even by the odd standards of the day. If a noble family in a particular locality had behaved like the Yorks did there would have been chaos in the region. One way or another they weren't normal, is my hunch. I don't know exactly what that implies for the princes, but I don't think we can take any normal relationships for granted.