Imagine a game banning you for being toxic and then steam banning you from all multiplayer games. Boggles the mind.
If Valve had the staff and Valve was the one handling bans from games, that's exactly how it should work.
People who aren't consistently making the experience of everyone around them worse don't routinely get banned, and a proper appeals system is more than enough. Being online doesn't mean that there aren't real people on the other end that you're harassing and treating like shit and ruining their gaming experience. "If you make an alt and go online, you lose offline access too" wouldn't be an overreach. It would just be good policy. You don't have a right to harass people with impunity.