I don't think Google is moving to disallow them, it's more that the EU said that it's fine for Apple to still own app notarization / developer verification even outside of Apple's app store. Google saw this and said, cool, we'll add that to Android too so we can also get our (undeserved) cut outside of the Play Store. I can install F-Droid or anything else, but if they dont submit papers to Google, I get a big scary warning when I install it (I get the same scary warning if a developer distributes apps through F-Droid, but doesn't verify with Google, which is ridiculous too). On iOS if I don't submit to Apple I cant do anything.

It all sucks, and I'm not saying this is a good thing. But Google and Apple are both trying to position themselves as not having monopolies on store fronts, while still forcing notarization and verification to run through them independent of the store being used. And the EU seems fine with this for some insane reason. Google isn't trying to be worse than Apple, they're trying to match Apple.