Without Safe Harbor - then what
Without "Safe Harbor" or its equivalent, almost all social media would be impossible. Not just the giants like youtube and facebook but smaller sites such as the register forums would not dare operate due to the chance of being sued out of existence.
As Youtube has over 300 hours of video being uploaded every minute, it is unreasonable to expect that all illegal content be detected and removed immediately. Its processing algorithms are good and remove much but inevitably some gets through the automatic filters and is only removed when a complaint is made. (To have a human watch each of the Youtube videos for illegal content would require a full time staff of over 100,000 - and how many of them would still be sane after watching their 1000th cat video!!! ).