As flawed as the DMCA is, it does a pretty good job of protecting the service providers themselves. They need to implement a timely DMCA takedown process but that's about it. They can still be sued but, to my understanding, mostly through stretch interpretations of existing copyright law created by legal precedent rather codified into law per se ("inducing copyright infringement").
So, and I ask this question honestly, how could the law be more open short of abolishing copyright? (Once again, DMCA takedown abuses notwithstanding.)