If a utility company is privately owned and it's denying service because you have 'different opinion about utility prices' thus threatening your life will you stand it?
No, we're not. Trump's tweets are still there. He retains the ability to post. All Twitter did was exercise their own free speech by adding a note below it.
Also I was not talking about the link being left, I was talking about your account terminated.
It may be good to raise the issue how much power social media should have, but please don't conflate the issue with personal vendettas of some public figures, or too much toleration of relativistic alternative facts.
I was specifically talking about this issue and it's the commentators that went to "personal vendettas or introduction of relativistic alternative facts."
Public universities have additional restrictions because they are organs of the state. Twitter is very definitively not in that category.