Also, there would be penalties for filing false or invalid DMCA claims.
https://www.law.cornell.edu/uscode/text/17/512 (search for "(f)" a couple of times)
It has been a very weak penalty in practice without much enforcement, but there are some examples of it being used:
https://en.wikipedia.org/wiki/Online_Policy_Group_v._Diebold.... (successfully, but with low enough damages that it was mainly a moral victory and not really a disincentive for anything)
https://en.wikipedia.org/wiki/Lenz_v._Universal_Music_Corp. (rather less successfully, but not only was the work allowed to stay online, the case did confirm that copyright holders must at least give subjectively good-faith consideration to the idea that material or activity may be fair use before sending a notice of infringement. this does not necessarily require a proper legally reasonable weighing of the statutory fair use factors, just subjectively good-faith consideration.)
Even in a perfect world where the DMCA is "balanced" and any abuses are properly punished, this problem wouldn't go away - the platforms will merely provide alternative means for advertisers (and anyone else who's happy to pay) - their real customers - to take down whatever content they want. It will merely become a bullet point in their list of features that they offer to paid customers, completely independent of the DMCA (and thus wouldn't be subject to whatever the DMCA says).
(I also don't know what theories hosting providers use or don't use to argue that they don't have §1201 liability for things that their customers post...)