Nobody complains they do that. The complaint is that that isn't all they do. Sometimes they take down material that they consider infringing without having received a notice, and they often get this wrong.

Many of the platforms have proactive DMCA applications that actively scan their own content. They have a non-zero false positive rate, although I have no idea what the probability is.

YouTube has its own non-DMCA process to streamline complaints and satisfy the rights holders who they want to maintain a business relationship with. If you don't have such concerns then basic safe harbor compliance is all you need.