I appreciate everyone using the word "publisher" to describe YouTube. Platforms only have legal protection from user content being their responsibility if they are not publishers. I would be happy for YouTube to lose their safe harbor protections if they continue to censor content.
The press you mention is legally accountable for its content. Platforms have protections. Telephone companies, for example, aren't responsible if you slander someone over the phone and they send the audio to the recipient.
Why shouldn't platforms be stripped of their legal protections (and some effectively destroyed) if they are exercising editorial discretion? Why shouldn't YouTube be responsible for the videos that they do allow/have approved?
If someone doesn't think that YouTube should be accountable for content, then should a newspaper be accountable? Should a person be accountable for his content?
This is actually an extremely gray legal area. The only reason platforms are viable is because they have legal protections that don't make them responsible for user content.
At some level of "taken responsibility" (which I think should have been passed), they should be considered publishers and be stripped of their legal protections.
Why isn't YouTube a publisher now rather than a protected platform?
Why couldn't the NYT justify itself as a platform instead of a publisher if YouTube is a platform?