> The constitution of United States, in the first Amendment prohibits certain speech, speech inciting violence is one of those prohibited speech.

No it doesn't. The First Amendment constrains the government from prohibiting most speech. It doesn't require any speech to be prohibited. If the US Congress wanted to be free speech absolutists, they wouldn't have to change the constitution.

> there are absolute cases when censorship is needed.

There are cases where most countries sanction it. That doesn't prove that it's needed.

Can you even name a case where it would be necessary as opposed to being possible to solve through e.g. vigorous enforcement of the laws against violence?

You're also avoiding the question. Sure, sometimes the same thing is illegal in both the US and China, but that's not the common case for free speech questions.

And putting aside the absolutist position, that's not even what you're arguing for here. The government can punish a direct speaker for imminent incitement of violence without imposing a prior restraint or putting intermediary liability on a third party who is merely a common carrier.