I believe they should be treated as a common utility, because this is what they are because of network effects.

In that case, I think they would be under obligation to not silence people like this.

You won't get much disagreement from me on that basis though I wish that was the reasoning they gave-- rather than the transparently false statements about leaked documents.

I'm also dubious about applying that to private messages: Twitter isn't a party to those messages, interception of the content is an unlawful wiretap. Without unlawfully monitoring the content of the users private community it's not clear to me how they could be suppressing the content.

They are free to do whatever they want with any message on their platform, private or public. If they were regulated as a common carrier, this would not be the case.

I believe that Twitter and Facebook have no desire to be regulated as common carriers.

There is no way this is an unlawful wiretap, as they own and operate the wires.

This is absolutely not true under federal law (18 U.S. Code § 2511.) (also apparently CA PC 631).

It doesn't matter who owns the facilities. Except for certain narrow exceptions (warrants, government officers, jails, incidental operations necessary for maintenance) any unauthorized third party interception of a private communication is unlawful. Common carrier status is relevant for liability but is irrelevant for § 2511.

I think you are confusing a Twitter DM with a private communication. Note that Twitter is not intercepting your DMs, they are the ones transmitting and storing them.