No, the solution is not recompiling. Nothing is gained from that. It's just checking and verifying compilations.

Obtainium can download apps from any publisher. Most apps just to happen to put their apk on GitHub, so that's why it feels like a wrapper.

The main point is that no one can block you from using the latest with Obtainium.

F-droid's compilation happen every 2 weeks or so. They don't seem to have any plans of changing that. They will always be at least 2 weeks late.