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.