I believe the idiomatic solution for “handing your child an iDevice but only letting them touch one app” is Guided Access mode.

It’s only when you want to let them jump in and out of multiple apps (e.g. pick what game they want to play on their own) that you start having a problem.

(And the not-idiomatic-but-people-do-it-anyway solution for that, from what I’ve seen, is buying one extra iPad, and creating a special whole-family Apple account for it, to effectively serve as a game console for the kids.)