Yes — because that's something reserved for privileged system apps. You have to root your device to take advantage of that, or make a custom ROM with the alternative store in it. Having that ability as a permission you could grant to any app is an immense security risk. But then there are "device administrator" apps that can literally factory reset the device... I don't know. Maybe package installation should be part of that. Especially now that the legacy permission model was taken care of — if you install an app that doesn't support runtime permissions, you'll get a list of its permissions with toggles next to them when you run it for the first time.
> you'll sit there for 5 minutes just approving install prompts every week
Unpopular opinion: well-made software that serves its user doesn't need to be updated very often. Remember how you bought a program on a CD and used the exact same build for years?