This whole thing is a question of degrees. I think "common carrier" was a useful concept: loss of control traded for immunity.
Edit: That said postal systems are generally owned by the government. So I suppose ultimately (if nothing else) it would be up to their T&C. But I don't see how they could reasonably justify monitoring the traffic. It's not like it's a PR issue for them what users share through their tubes. I would imagine it'd make sense to have them regulated similarly as the postal system (ensuring private communications).
https://opentodebate.org/debate/mock-trial-murthy-v-missouri...
The first debater said it was okay because the companies complied voluntarily. I found myself at first nodding along.
Then, at least for me, after hearing more arguments I was like, "okay, she's basically saying if President Trump calls Musk and says (please censor anything pro-Biden)" that's fine as long as there's no "or else". To me it seemed wrong for that to be ok.
The other debater also pointed out that even if there was no explicit "or else" the twitter files made it clear the people there thought there was an implicit "or else".
It's a hard problem.
The government should not make any speech illegal on a federal level, but individual private businesses or websites (like HN) can still decide what's tolerated on their property.
And the corollary -- I believe in free speech but there are some people I'll never listen to, even though I believe in their right to speak.