No, this increases the overall complexity of the system. Android will hopefully eventually collapse under its own weight.
Could you explain? I don't understand what you mean here. https://f-droid.org/F-Droid.apk is signed by the same key that signs https://f-droid.org/repo/entry.jar
Why not download source, review, (edit) and compile on the device, e.g., using Termux, Gradle and Android cmdline-tools
Is "convenience" the rationale for the F-Droid app
Maybe it's the same rationale that drives Linux users toward "binary package managers"