The DMCA policy and registered agent gives a content creator a method to notify Y Combinator of the violation so YC can take it down. How else would they know who to contact or how to protect their rights?
If a site has a proper policy and agent (and abides by the policy) it gets safe harbor - it's not liable for the infringement. It's not an unreasonable amount of effort, and the scheme is a pretty decent compromise between protecting copyright holders rights and allowing user generated content.