Why I built it: I wanted a safe, ad-free environment where my kids could see themselves as the heroes of their own adventures.

This is what play is for. I don't think trying to maximize engagement by training them to see themselves at the center of events is a recipe for healthy mental development. If you're not finding that standard bedtime stories are sufficiently engaging...try different ones? It's not like there's a shortage of children's books, maybe your kids are in the mood for more advanced reading material.

one of the key benefits of reading non-personalized stories is developing an ability to appreciate and mentally model things that are happening to other people, albeit fictional ones. The reader not being in control of the story (and indeed feeling powerless to change the outcome) means they're forced to engage with the possibility of things not turning out as desired.

If you want to help them capture their unique imagination, buy them a tape recorder. Writing and drawing their own books at that age is a tall order because it's such a time-consuming process, but chattering isn't a problem, and they'll probably figure out how to iterate on things by themselves.