With all the PWAs I've been seeing lately (Mutiny, all the Cashu stuff, Nostr), there should be a Bitcoin and Nostr-centric progressive web app store.
Discussion
Umbrel and the like have this already but Bitcoin store for mobile would be grand.
The reason these are PWAs in the first place is to circumvent app stores though. If an app store allowed them they wouldn't be PWAs but native apps.
This is the closest thing to your idea. Great project being built to shed more light on PWAs.