I mostly don't disagree with you, but I think it's precisely the "illiberal mob[s]" you describe that are most threatening to open discourse. You may not be able to destroy ideas, but you can sure make it difficult for them to flourish.
An example from the left, this time: a year or two ago, an Asian woman (Amelie Wen Zhao is her name, IIRC) wrote a YA novel whose premise involved a) a completely imaginary society based more on an Asian cultural background than anything else, and b) human enslavement. She was attacked by a disgusting social media mob hailing from the YA "community", who used both covert (backchannels/"whispernet") and overt (calling her a racist on Twitter and whipping up a controversy, apparently without actually having read her book) means of attack, justified because (according to them) slavery as a topic/theme in literature is reserved for black authors. These attacks were so violent in their extremism that at the time I swore up and down they were mostly "Russian bots", and I still don't know.
Anyway, I'm not black, nor Asian^[1], but this just seems crazy to me. She did initially delay the publication of her book and could easily have canceled it entirely. This is what I mean by shouting down ideas. I (an amateur novelist) see a lot of forum posts from new writers asking what they can and cannot write about, worried about exactly what happened to Zhao—how many great stories have gone untold because of this insanity?
I think this effect manifests a bit differently on the conservative side—they simply refuse to acknowledge the truth or directly address arguments, and this codes as strength to people who share their ethic. I mean, I think extremists on the left do this too, but I feel like righties are more comfortable with this aspect of their nature, less concerned with virtue signaling and more with active expression of antisocial values (e.g. "rolling coal" on cyclists is funny, ha ha).
So, again, I do think we mostly agree. But how would you suggest we foster an environment where these illiberal mobs don't have power, without censoring/censuring them and their speech somehow? This seems really important, because by their nature these groups seem to be the most interested in gathering and holding on to power over the discourse.
^[1] I capitalize 'Asian' because it's derived from the name of a continent. I doubt I'll ever capitalize 'white', because why would I? and I'm not on board with 'Black' yet either, just from a linguistic point of view. I mean no disrespect by it, and I'd love to hear arguments as to why I should drop that capital B in there, because I'm sure this is going to get me in trouble more and more going forward. But so far (and yes, I've done some reading) I'm not convinced.