It would be entirely reasonable for Youtube to block them from submitting the current style of claims and require them to submit actual, proper DMCA claims which open the claimant to all kinds of counterclaims, require the claimant to assert under the penalty of perjury that they own that content, etc.
That's an idea for sure. I should have clarified my point that while these aren't DMCA claims, YouTube is required to handle DMCA claims, and their current process essentially preempts them. So that's how they're choosing to effectively 'handle' what would otherwise presumably be large numbers of DMCA claims.
But yeah, maybe requiring claimants to actually go through the official process would be better (albeit more work for YouTube).