If a claimant makes a bad-faith claim or the claim is done by undersupervised automation? Sure. But I think some of these claims are false positives by YouTube's ContentID system. In those cases, does YouTube pay? I agree there needs to be a disincentive to over-claiming (including but not limited to holding ad revenue in escrow and returning it to the video's owner if the claims are false) but in practice, I don't know how it needs to work.
If its an automated system, then yes I think youtube should have to compensate users when the system youtube created, screws over an innocent user. If the government, who is almost as powerful as google, similarly created a system where they falsely arrest huge swaths of innocent people, then they too should have to compensate their victims. The goal here is to get youtube to do better, and the only way to do that is economics.
