https://googleblog.blogspot.com/2007/06/state-of-our-video-i...
Do you have a source that says they were forced to do it by outsiders? Or any plausible way in which the DMCA required that?
Edit: also, content ID is automated checking of uploads. The ability for copyright owners to take down content directly is under a different program, I think.
Google is basically volunteering to allow people to issue take down requests without consequences; if it was an actual DMCA take down, they would have to
And yes, Content ID is another system entirely where Google pattern-matches uploads (and old stuff when they feel like it); when hits are found, Google tends to reasign the monetization to the "content owner" that registered with Content ID. Getting that money back has generally been impossible, even in cases where Content ID clearly screwed up (false positive).
If you're interested in the history of how Google has been using Content ID, there is an older discussion[1] from a few years ago when Google really started to abuse Content ID hard.
So YouTube introduced content id to show that it really was taking copyright serious, and not just using plausible deniability.
Viacom mostly lost the case because there never was much better evidence that YouTube employees knew about individual copyrighted videos on the site.
Google probably keeps the system to avoid new suits and to make business partners happy. A lot of Google content isn't crowdsourced anymore, it's uploaded by big business suppliers who are essentially business partners. I imagine those contracts include content id to be used.