If you get a takedown notice you have little to gain and much to lose by filing a takedown notice. It’s unlikely that the copyright owner will sue (source: private communication) but if they do then you will end up in a world of pain, because your legal bills will be crushing whether you win or not. Winning does not enable the user/uploader to recover legal fees.
So here is a spot fix to the DMCA that would make a big difference: if an uploader posts a counter notice, the copyright owner sues, and the uploader wins in court, the copyright owner should pay the legal bills.
If this happened, lawyers would take some cases on contingency, and filing a takedown notice would come with risks.