No where in the Safe Harbors does it say it offers protections for Websites. The DMCA was passed in 1998. In 1998 there were 10s of millions of websites, if not more.
If the safe harbor laws were meant to apply to Websites across the board, they would have used the term website and its broad definition, rather than the words ISP, OSP and Service Provider to define those elgible under the safe harbors.
I know it seems like the dark ages to some, but even in 1998 there was a ton of user generated content. Pictures, Music, and even Video was uploaded, streamed and downloaded. It wasnt as neat and clean as it is today, but it was there. It was in usenet groups. It was in AOL Chat Rooms. It was in CompuServe and Prodigy Forums. It was on audio and video hosting sites. There were sites that kid put up that hosted or deep linked to thousands of streams or downloads. They weren’t nearly as fast or easy as today, but in principle they were the same.
If the goal of the DMCA was to protect every website that enabled the uploading of User Generated Content, take my word, all the politicians, as firmly rooted in the back pockets of the media companies as they were and are, would have explicitly used the term website.
They didn’t. They didn’t by intent, not by omission.