No, but they'd need to pass laws and fight court battles to enable censorship versus merely taking over existing systems of censorship. The latter is much easier to do and much harder to notice or right against. Especially when merely fighting against it is grounds for censorship.
>Yes, but on the other hand, the prevalence of far-right dialogue contributed to the rise of far-right politicians.
Depends on the scale you look at. In a sense, the far right is merely the average person's view as of 50-ish years ago. Censoring to the view of the average person merely ensures that in 50 years you'll be seen as having helped far right ideas. Or in a different way, I don't believe that my current views are the pinnacle of progressiveness (or morality or whatever) and I am loathe to prevent future progressives from being able to push their views forward.
I don't think that's a significant hurdle to any politician with popular support.
Look at Trump, for example, not because I hate him (well I do, but that's not the point here), but because he is a good example of what a politician can do. He rammed into the freaking Supreme Court a candidate that was accused as rapist. And there was nothing the opposition could do.
And the crazy thing is, Trump doesn't even enjoy unanimous support. Far from it.
There's not much you can do once a politician is at power, has a semblance of popular support, and is willing to forego established political norms. Laws? They will change laws, they will take their matter to courts, and they will win.
So I'm still not convinced it's a net positive to have an uncompromising legal roadblock against censorship, when the cost is to increase the chance that someone will rise to power and kick that roadblock away like a tin can.
All things considered, I'm not convinced that censoring extreme far-right contents is a long-term net negative for freedom of speech. (Well, it could be, but it's not a given.)