Android does provide this. Your app can send out a message on the system: "i need a picture" and usually the built-in camera-app will accept the request, and send a picture back to the requesting app (which then does not need camera permissions since it, itself, never accesses the hardware).

This feature is actually quite foundational to the Android architecture, where the vision was a bunch of small apps working together in this manner.

Unfortunately it's a slightly more clunky user experience than what users these days have gotten used to: big monolithic apps that handle everything themselves.