For example, there's this notion that the advancement of knowledge is somehow being suppressed and that naked, barely-regulated free speech has been essential to Western dominance, and that, accordingly, to backpedal on the principle would have some material affect on society.
However, no nexus between the kinds of speech and people being "cancelled" and any sort of practical benefit of the speech is ever identified. Nor do they consider the fact that the proper result of intellectual discourse is that some ideas get discarded, and that to constantly have to rehash debates, reestablish the credibility of basic authorities, etc, drags down intellectual discourse and in fact moves us backwards.