Knowingly filing false DMCA claims will also perjure them.

However, ICANN has a whole procedure they follow where complaints are fact-checked, whereas DMCA takedowns put an unreasonable burden on hosting providers that requires immediate action, and many hosting providers will take such action automatically to protect themselves.

I doubt they care about perjury. They care about results, and the DMCA gets them exactly that.

The phishing reports are interesting, providers aren't necessarily required to act as fast on those. Although, I suspect companies like Cloudflare who get used by countless phishers will probably also set up some kind of automated anti phishing system.