They would - and and they are. That's why it's easier to publish fanfic on the internet than with an actual publisher. Tumblr is not on the hook for unauthorized titillating usage of copyrighted Disney characters, but HarperCollins would get sued to bankruptcy if they attempted the same. This is why the calls to repeal section 319 is idiotic - it will lead to more "censorship"
The argument is that, instead, these other, non-publishing, major communication platforms should be treated how we run other major communication platforms in the past, such as the telephone network.
We have existing laws, that could be extend to cover other communication platforms.
Telephone companies have been required to do certain things for decades, and the world hasn't collapsed because of it.
The argument is that moderation should be done by publishing companies and who face liability for their content. It should not be done poorly, en-mass by platform companies who do it at scale using automation and don't face legal liability when they mess up.
The only exception I see to this is to allow community organized and run moderation for noncommercial communities.