The way people on YouTube get around the legal penalties for false DMCAs is simple: they don't file a DMCA request. There are several other mechanisms by which YouTube will gladly pull content: Content ID, contractual obligations, TOS violation, etc.
They just don't care. They're not a public service altruistically serving their users' videos up until the point the law requires them to take it down. They're an ad platform, trying to serve ads and not get sued.
That is part of the DMCA (the act, not the "DMCA notice" often shortened "DMCA"). In exchange for not being liable for the copyright infringement ("safe harbor"), the service provider (here YouTube) has to act on notices right away. The user files a counterclaim if that was wrong.
In short, it's not YouTube's (or GitHub's, etc) call, this is part of the agreement with copyright holders (the DMCA copyright law).
Don't take that as an endorsement though, I hate the system as much as you do.
Money, dear boy. They gain a lot more from keeping the big media companies onside than they do by pissing off a handful of creators (who are frankly a commodity to them).