Establishing certain mass-DMCA senders as often fraudulent would be risky to do without at least a summary judgment, so YouTube, Google, Twitter and ilk provide no pushback against repeat DMCA notice fraudsters as any perceived pushback could land them in court.
Under Section 512 the only responsibility of the service provider is to remove the content, relay the notice to the actual copyright infringer, and allow them to file a counter-notice.
From there if the counter-notice isn't accepted by the copyright owner, they would have to file a lawsuit with the copyright infringer.
But can you as the alleged infringer sue the claimant?
I think the original question is if the platform can sue the person sending the DMCA takedown, for some kind of harassment. Because the platform itself will also investigate before taking content down.
Essentially the belief is that DMCA would never be abused for any reason so you need to penalize the platform but not the submitter.
https://en.wikipedia.org/wiki/Online_Policy_Group_v._Diebold....
The penalty wasn't big enough to have much of an impact on anyone involved, after lawyer fees. But damages were awarded.
EFF's legal director is quoted in that Wikipedia article discussing that case, so I presume EFF has either a legal or a strategic/PR/financial reason why they can't use that provision in this case.
I'm not a lawyer myself, though I have attended a year or so of law school and I have read the text of the DMCA.
I don't think I've heard of a single civil or criminal case under the DMCA's false notice provisions. It's effectively hot air.
I'm not saying the little guy shouldn't sue; people should stand up for themselves whenever they are accused of wrongdoing, and especially when they know for a fact they are innocent. The problem is, even when suing and winning sets a precedent, the big players just move the goalposts again. There's never going to be an easy solution that satisfies both content creators and content consumers short of massive copyright reform and hard criminal instead of soft civil penalties for making bogus DMCA claims.