Earlier quoted context omitted.
IMO the biggest issue with all this is the lack of a suitable appeals process, handled by humans. Would such a process be expensive? Yes, but you can't have it both ways, enabling copyright holders to lodge spurious claims at will, and not allow content creators - who the entire platform is built on! - to disclaim them. Would such a process be expensive? Yes, of course - but YouTube can very well afford it.
I think the biggest issue is that the burden of proof and all the risk is on the person who's video is being claimed. False DMCA claims are free, practically riskless, and require no evidence.
This is the crux of the issue. The DMCA needs to be amended so that filing an incorrect claim comes with some risk.