This already exists; apps have to opt-in to using it and a Facebook (among many other apps) refuses to.

This is already how apps access files (except for files in the app's own directory). Don't see why Apple couldn't make it work the same for photos.

It does, but apps want to customize the experience instead of using the OS provided picker for some annoying reason. At least they should fallback if you deny access to your library, I’d like to see Apple mandate that.

Android has "intents", which do exactly this. But you need to explicitly code against that.