Why isn't the same warning shown when installing from the play store? Apps installed from the play store can have the exact same permissions as side loaded apps. You can claim that Google vets the apps, but this is pretty much false. Just go make an app and experience the process for yourself, it's laughable. Any checks they perform are automated, and there's no reason those couldn't just run on-device.

And besides, even for side loaded apps they have a database of "bad" apps that get deleted by Google called "play protect"

So you've gone through all the weird flows to accept and enable installing. Now how do you get security updates? Google scares them again every time, even though android apps can already execute arbitrary downloaded unsigned code at runtime (otherwise V8 and other JITs that generate machine code can't work), so it isn't really protecting much and mainly makes things more insecure by not letting you add your own trusted providers permanently for timely updates.

Something like enabling instant apps and play protect scanning for any apk on the web could mean a nicer and safer experience for users. I think people would still use the app stores for their discovery/convenience but safer web installs could be an option for both users and developers.

This model exists on desktops and laptops, where there is signing or browser scanning, just not on mobile.

To be fair, installing an app from the store might be harmful too.