Isn't one of the largest benefits of DMCA the safe harbor protections? Like you said, copyright law exists without DMCA, in which case the Githubs and Youtubes of the world could be sued.
But I don't think safe harbour was entirely new with DMCA - it's a formalisation of what was there? Wasn't there some cases in the 90s where free web hosts and isps were found to not be responsible for users hosting copyright material? Maybe I misremeber.