But there are penalties for false claims. There is a fine for claiming copyright you don't own, and if you go further and ask for takedowns, you are also liable for damage.
The problem is that these are rarely enforced. Even a $100 fine for a false claim on YouTube would be enough to weed out bots and click farms. And for the most serious cases, have the infringer pay damage and a bigger fine. No need to change the law for that, it just has to be enforced.
Consider the penalties given for a crime, and compare those to the penalties given when police or prosecutorial or judicial misconduct falsely, incompetently, or corruptly imprisons someone for that crime.
The latter are overwhelmingly more rare, but overwhelmingly larger. Society in general thinks false penalties for crimes are worse than the crime itself.
"It is better that 10 guilty men go free, than that one innocent man should suffer." I think that if the penalty for copyright infringement is $250,000, the penalty for a false claim should be $2,500,000.
You're right that a $100 low-effort, frequently-enforced counterclaim process would weed out ContentID bot farms (just like a $0.01/email transaction cost would weed out spam). But remember that the whole ecosystem is already ridiculous; if the pro-copyright MPAA/RIAA are pushing for $250k/infringement you have to be equally ridiculous to balance counterclaims.
That's an argument to reduce the penalty for sharing a single music file, not for making the penalty for a false report also ridiculous.
Then again, I personally do think that knowingly filing a false report of law-breaking should be treated as a very serious crime. I think the harm of filing a false report of copyright infringement is greater than the act of infringing copyright itself.
