Then they are the target, and will incur many costs. Fine once, maybe, but what about the tenth time? The hundredth? The thousandth?
It's like wanting Google to be the legal shield for everyone committing copyright infringement on their sites. It's not remotely economically feasible.
Not having safe harbor would mean that if anybody posted content to GitHub that did violate copyright, GitHub would be liable and would end up having to fight in court. Even if they won, they would be expending massive amounts of money and effort fighting copyright battles.
These battles wouldn't even be fought "on behalf of their users", because the entities taking them to court would also be taking the end users to court.
Without safe harbour GitHub could be sued for any copyright infringment that any of their millions (?) of users do. It would be a terrible business decision to give up safe harbour.
It's like wanting Google to be the legal shield for everyone committing copyright infringement on their sites. It's not remotely economically feasible.