Google Play already does this, though. Well, it used to, but now it’s throwing errors when I try to update apps.
I think this just changes the installer package stored by the package manager API so they can skip a permission prompt somewhere. Without that, you’d need to hit “OK” for every update you receive, like on older alternative app stores that don’t have the Android 12 API enabled yet (F-Droid, for instance).
Unless Google is willing to risk a DMA fine, other app stores should be able to do the same.