I don't even think open sourcing Minecraft would hurt them financially. People don't buy Minecraft because that's the only way to play the game; it's not, it's easy to find ways to run Minecraft for free. The reason people buy it is to join servers.
Most serious servers only allow players with valid paid Minecraft accounts to join, because it allows the server owner to ban people or otherwise keep track of people. I don't see any reason why this would change just because the game client was made open source.
People could set up 3rd party auth systems and eliminate the need for mojang
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