I'd love to know what would have happened if Henry had simply been happy with a female heir! He could have been. There were men around him who were starting to educate their daughters to high levels. His own grandmother was an absolutely formidable woman; there were plenty of real battleaxes amongst the female nobility both past and present. Catherine of Aragon's mother was a queen in her own right. Etc. etc.
If Henry had been a different sort of person, he might have believed Mary would be a perfectly acceptable queen, and he could have started laying the foundations to make her authority unquestionable, bringing her up to be a ruler, and so on.
My (totally speculative) sense is that he wasn't able to do this precisely because no one had ever really prepared him to be king. Because his older brother was expected to be crowned, Henry had nothing to fall back on except the belief that somehow, God and fate had made him king. And I think that made him horribly insecure and nervous in a way he might not have been, had he been brought up to believe he was always going to be king one day. I think that meant he was also totally inequipped to see that his daughter might be a ruling queen.
I can imagine Henry growing old and fat and boring with Catherine, who was absolutely devoted to him, and staying in the Catholic Church.
I love the idea of how different the rest of the sixteenth century/early seventeenth century would have looked in a Catholic England. Instead of Shakespeare et al. writing plays about spooky, conspiring Catholics with their superstitions and their weird Spanish/French/Italian ways, we'd have have plays about spooky, conspiring Protestants with their superstitions and their weird German/Swiss ways.