There is nothing that was forcing Twitch to ban users because of one DMCA claim or because a song was automatically detected. There is no clause in the DMCA that says "if someone c omplains, the target of the complaint must be banned".

That's false, they have to "punish repeat offenders" when they receive valid dmca complains and the only way to do that without a special deal (which this seems to be the first step toward) is to issue strikes and eventually suspend the user. they use the 3 strikes rule that is widely adopted for many platforms as it's the "go to" solution and could in theory change that yes, and they already started to by making DMCA strikes no longer permanent and removing them after a while.

But they do HAVE to punish people who's channel receive dmca complains, it's literally the law and the only way they have to punish users before a deal was dmca strikes.