Respectfully, I think this is the wrong fight. And I fear it may be counter-productive, because all the effort put into asking Google to make it a little less painful to install an unverified app is not put into the real fight.
IMHO, it should be fine for Google or Apple to do whatever they want with their OS. What should be forbidden is to prevent people from installing an alternative OS on their hardware. But this is not all Google's doing there: all the Android manufacturers are actively preventing users from doing it.
When I buy an Android phone, I should be able to unlock the bootloader, add custom signing keys, install whatever OS I choose, and relock the bootloader. Interestingly, currently this is possible on Google Pixels, but not on most other Android devices.
When I use an Android phone, a company building an app should not be allowed to ban my OS "because it is not the Google OS". That is, using Play Integrity or whatever they do to ban alternative OSes should be forbidden. But again, this is not entirely Google's fault: the companies choose to add those checks in their ** app. And it is a bigger problem there, because while I can install an alternative OS on my Android device (e.g. GrapheneOS or LineageOS), I can NOT install an alternative client for e.g. my bank.
Back to side-loading: really it's mostly a problem for F-Droid on Stock Android, as far as I can see. And really, people who care about using F-Droid would probably be happy to use an alternative OS, if it was reasonably possible. We should fight for that.