Even if we disregard the obvious costs of having thousands of people screening uploads all day long, I don't think it would work better. The humans will need to identify the content, and decide if it's public domain or not. This requires an infinite amount of knowledge, or a lot of googling.

I think a hybrid sollution (computer identifies the content, and if it is not sure about it being public domain or not, a human is used to give the final verdict) is probably the best compromise. But I expect that YT is already doing this.

AFAIK the first copy right takedown noticed is received without review by Youtube, they only review after being contested.

From my perspective, people are just too used tolerating the bad things of ContentId which in part is the result of bad legislation.

In this case I bet that no human would be able to make a confident call because of multiple jurisdictions. On Germany it's public domain but on France maybe it's still copyrighted so you need an international copyright law master degree to figure that out.