I imagine they do this because of their settlement with Viacom[0] where they likely bent over backwards to avoid further appeals and lawsuits. Viacom likely said "regardless of how this goes, we and other copyright holders will sue YouTube off the internet unless you build a system that proactively takes down everything even remotely potentially infringing without us having to notify you of anything". And Google caved.
Don't get me wrong, the DMCA is still overall a bad law (though, to be honest, I think the copyright takedown process is the least bad part of it), but Google is not doing what they do because of the DMCA.
[0] https://en.wikipedia.org/wiki/Viacom_International_Inc._v._Y.... -- notably, no money changed hands as a part of the settlement, but other terms were not disclosed.
And you know who can afford lawyers? Big corporate copyright holders.