Precisely, the problem isn't Twitch implementing this. It's the copyright system that forces them to do this.

No, it really isn't. Under the DMCA they are free from liability if they just sit there and respond to DMCA requests as they come.

Someone could set up a bot to send DMCA requests under the same algorithm, but they'd be guilty of perjury if they lied.

That stops being realistic when you get to the size where you have thousands of DMCA requests coming in a day.