YouTube and so many user-generated sites get around this with the excuse that "It was a user who uploaded it! It doesn't matter that our servers are holding it, promoting it, and playing it for everyone, and that we know this will keep happening ever minute". It doesn't matter that it's their sites who get the majority of all DMCA takedown notices.
What if the smaller players just started modelling their sites on the user-generated ones? And upload the content as if it was just a user, and when they get a DMCA, they take it down, and just re-upload next week.