Android will block any update to an existing app that wasn't signed with the same signature. The benefit of using the developer's signature (even if the app is built by F-Droid) is that the F-Droid release of the app is not treated as a "different app" by the Android OS, and thus it can be updated by other app stores or through direct APK releases from the developer. If the user chooses to stop using F-Droid in the future, they can still receive updates through other means without uninstalling and reinstalling the app.
It also allows the user to place a little less trust on F-Droid because the developer, as well as F-Droid, must confirm any release before it can be distributed. (Now that I think of it, that probably creates an issue where if malware somehow slips in, F-Droid has no power to remove it via an automatic update. Perhaps they should have a malware response or notification system?)
More: https://f-droid.org/2023/09/03/reproducible-builds-signing-k...