Honestly, it might not be terrible idea. But it should be relatively cheap (3-5€) and accompany the current 1 month ban. Meaning you'd still be banned for a month but additionally have to pay a small amount of money. That way shared alt accounts will only be used to cheat once because nobody will want to pay for them. Also people will think twice about cheating on their account after that, I've seen many hackers just a few days after they got unbanned. I don't think there needs to be a third chance for players.
Edit: Also I have no idea if this would violate the EULA, I guess they'd have to ask Mojang. Technically it's not paying for an in-game advantage or access to a part of the server, but paying for access to the server at all which is generally allowed. Not sure what Mojang's stand on that is though.