I am not saying it justifies locking down devices, but that's the kind of situation where I think a bit of friction is a good thing. For example having to connect your phone to a computer and run some command line tool (like for unlocking a bootloader). You still have your freedom, but it is also something you are less likely to do by accident. In the sideloading situation, it looks like you could make yourself a developer account and repack apps under your own identity, which is one of these high friction workarounds.

For F-Droid specifically, maybe they should negotiate with Google before going to the offensive. Maybe they did and it didn't work, but I think a good compromise would be to let F-Droid has a key to sign the apps they compile, making F-Droid accountable for the apps they distribute.

And by the way, Firefox is in a similar situation for extensions. Over the years, they made it really hard to install anything from outside the official Mozilla repository, citing security concerns. It is not just Google.