So in that case, wouldn’t the right way to handle it be to get a warrant to have Cloudflare give you the identity so that they can be prosecuted under copyright law? And if there is no law being broken, Cloudflare doesn’t have a responsibility to do anything. You wouldn’t want a company to reveal your identity just because someone asked nicely. You’d want a judge to approve a warrant.

Yep, I would say so

The protection these dodgy sites enjoy also protect a lot of other sites that could be quickly removed with simply enough capital, even if the legal claims had absolutely no basis.

Yes, it isn't optimal, but the advantages of hosters not carelessly taking down other sites makes hosting a few bad apples worth it.