There are protections against false DMCA claims. I think a false DMCA claim is actually perjury.

The thing is though, the vast majority of claims on YouTube are not DMCA. YouTube has their own extra-legal system called Content ID. Where a DMCA claim carries the force of law and requires the allegedly infringing content be removed from the platform, claims under Content ID are essentially a contract with YouTube, and they give the claimant the choice of taking the video down, muting it (if the allegedly infringing content is audio), or monetising it and taking all the money for the claimant. They can also do different things by region, which is why at least historically a lot of videos were taken down in Germany but available elsewhere.