Earlier quoted context omitted.
All Apple has to do to fix this is allow sideloading. They don't need to change the App Store's rules—they can make them more stringent, actually—and you can set up your child's phone to block non-App-Store installations. Heck, Epic would probably cave and accept the cost to keep Fortnite in the App Store; they tried to go around Google Play, and it seemingly didn't work out.
The problem with that is that it is all or nothing. The milder approach I had in mind was that apps require you to register an account outside the app (like amazon) but the purchase is initiated inside the app and outside Apple api. At the beginning that will be easy to simply not register and not use games that require registration. But well, micro-transaction started that way and nowadays all the major player do it…
Unlike current Apple policies?