You can already do that and some do. Mojang, for some incomprehensible reason, even lets you disable auth in the official server's settings (`online-mode=false`).

It's not incomprehensible. It enabled LAN games without outside internet access.

Maybe, but the "paying" is load-bearing, because you need to prevent banned people from just creating new accounts.

Sure a different approach might be possible, but would likely also hinder adoption of such a 3rd party account system.

That already exists, but people still buy the game