As per another informative response in this thread, that is allowed by various court rulings, even if it is not a great look.
https://reason.com/volokh/2021/07/19/when-government-urges-p...
> [A.] Generally speaking, courts have said "yes, that's fine," so long as the government speech doesn't coerce the intermediaries by threatening prosecution, lawsuit, or various forms of retaliation. (Indeed, I understand that government officials not uncommonly ask newspapers, for instance, not to publish certain information that they say would harm national security or interfere with an ongoing criminal investigation.) Here's a sample of appellate cases so holding:
> [B.] On the other hand, where courts find that the government speech implicitly threatened retaliation, rather than simply exhorting or encouraging third parties to block speech, that's unconstitutional.
> [C.] Does it matter whether the government acts systematically, setting up a pipeline for requests to the media? One can imagine courts being influenced by this, as they are in some other areas of the law; but I know of no First Amendment cases so holding.
> [D.] Now in some other areas of constitutional law, this question of government requests to private actors is treated differently, at least by some courts. Say that you rummage through a roommate's papers, find evidence that he's committing a crime, and send it to the police. You haven't violated the Fourth Amendment, because you're a private actor. (Whether you might have committed some tort or crime is a separate question.) And the police haven't violated the Fourth Amendment, because they didn't perform the search. The evidence can be used against the roommate.
> But say that the police ask you to rummage through the roommate's papers. That rummaging may become a search governed by the Fourth Amendment, at least in the eyes of some courts: "the government might violate a defendant's rights by 'instigat[ing]' or 'encourag[ing]' a private party to search a defendant on its behalf."
> Likewise, "In the Fifth Amendment context, courts have held that the government might violate a defendant's rights by coercing or encouraging a private party to extract a confession from a criminal defendant." More broadly, the Supreme Court has said that "a State normally can be held responsible for a private decision only when it has exercised coercive power or has provided such significant encouragement, either overt or covert, that the choice must in law be deemed to be that of the State."
> So maybe there's room for courts to shift to a model where the government's mere encouragement of private speech restrictions is enough to constitute a First Amendment violation on the government's part.
So basically it sounds like this could be the makings of a very fascinating case, if it holds up in court, but there is ample legal precedent of the government doing pretty much what happened on Twitter, already.
> No different than your local cops coming to the bar you like and asking for you to be kicked out.
Would that be ok?
I may not like it, and it may not be morally okay, but I am almost certain cops are able to do that, because that is the system we have created.