Establish the identities of people is something the courts have long had to deal with and is nothing new for them.

Indeed. But it's not something that Google can do, so bolting on an identity verification requirement to the DMCA process isn't helpful. Re-routing DMCA requests through the bureaucracy of the courts might work.

If counterclaims require doxxing yourself under penalty of perjury, then I would assume that's still perjury even if the other guy started it, so just making the counterclaim process easier doesn't fix the problem.