I think what should happen is this:
Step 1: Someone files a copyright claim (or perhaps this is done automatically). This is free.
Step 2: Someone disputes the claim. This is also free, and automatically restores the video.
Step 3: The filer can re-submit the claim but they have to post a bond for the price of a professional manual review by a trained copyright lawyer; maybe $1000.
Step 4: If the video owner can re-dispute the claim; to do so they also have to post a bond for the price of a professional manual review. The trained copyright lawyer comes to a conclusion; whoever "wins" the ruling gets their money back, and the other person pays for the whole thing.
If the video owner doesn't go on to step 4, obviously the copyright claimant gets their money back.