I definitely can see a “store is just an app, you must allow third party apps” as a sort of maximal approach. But treating app stores as a sort of special thing that requires extra permission and coordination doesn’t seem totally impossible.
It could be sort of nice if each store was isolated inside a different sandbox and had it’s own filesystem. (I wouldn’t be that surprised if something like that happened because it is both justifiable from a security point of view, and also mildly annoying for people who want to use third party stores, which I guess Apple would prefer).