The phone company was.[1] TV networks were.[2] And while there is still some debate about this, net neutrality would apply that obligation to ISPs. Why not Facebook and Twitter?
Radio and TV use public resources (EM waves), to which they have been granted a government license, to transmit information, so the government can ask them to do certain things at times.
These were regulated monopolies.
Then things get broadened because yes, that is copyrighted stuff being shared, guess we should stop that. Yes, if that revenge porn isn't illegal it will be soon, guess we should block that. Yes, if they literally chose a nazi flag as their logo we can agree they're a hate group. Yes, that user's post about the smooth taste of Lucky Strike cigarettes does look like it was upvoted by a botnet. Yes, we could probably detect those rape threat messages you received and block them, senator.
And before you know it, you're adjudicating whether that person was joking when he said he'd blow up the airport for cancelling his flight; whether that 'parody news' website claiming vaccines cause autism is clearly enough a parody; and whether the letter Q is a hate symbol.