Punitive damages is a thing.
The Supreme Court has suggested a soft limit, suggesting, IIRC, that it is rare that an award of more than a single digit multiple of actual damages will satisfy due process analysis.
What is the cause of action here allowing damages, punitive or otherwise? Stating a copyright claim in a DMCA takedown notice based on a different reading of how the four factors of fair use, which the statute doesn't explicitly set standards for or any details on how they interact, differently than a court later interpreted them?
Sure, if the court viewed things your way Netflix would lose a copyright infringement case against you, but that's about it.