>It's abused to take down content that's not in violation of copyright
That's a problem with DMCA in that it's applicable in an immediate and unilateral manner and any decision to resist comes after the takedown. DMCA is the problem in this context, not "copyright" itself.
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The real problem is that misuse is not followed by ruinously high penalty. False claims should result in statutory damages of tens thousands per claim. That is the way to prevent misuse.