> But they don't, because the former would require them to perjure themselves, and the latter just requires them to lie to a hosting company.

Doesn't stop anyone with DMCA... DMCA is coming up on almost three decades of being a law, and requires statements made under penalty of perjury.

However many millions (likely billions) of DMCA takedowns issued, who knows how many false/bad faith... I wonder how many have led to prosecutions for perjury, even when filing tens of thousands, en masse...

No need to wonder, the answer is simple. Starts with a "Z" and ends in "ero".