But in quite a few high-profile cockups recently, the VICTIM of the takedown is the copyright holder. So yes, this COULD work.
I'm in the UK, so if I found my stuff being taken down I would probably sue in the small claims court. Cheap and simple. And very expensive for whoever is doing the takedowns - not each individual case, but it would be "death of a thousand cuts" if the affected little guys kept suing.