The latest is that Google is making it easier for external stores. This was in development before their recent court loss against Epic. F-Droid is still going strong imo, although it’s certainly lacking as a place to browse for apps.
If F-Droid did die something would definitely pop up in its place. It already has a protocol that allows you to monitor other app sources than the official F-Droid store, such as directly from developers. Hell, there are already alternate versions of the F-Droid app, eg AuroraDroid.
All F-Droid does is vaguely check the app and then compile it with their key. They’re simply a single point of trust for this action, a buffer between the user and the many developers writing apps. This is a service anyone could provide, however right now no one else needs to because everyone trusts F-Droid well enough for most things, and their favourite app developers enough to update directly.
Also you need to keep them clean to maintain efficiency. In a field that’s easy - you can probably just employ the landowner and buy an attachment for his tractor. On the roof there isn’t really any good way of automating it, and some rooftops aren’t accessible for a window washer and a long brush.