IMHO a certain amount of this calling for censorship is people from those self-same institutions refusing to look at their own role in undermining the trust basis of our society. How many mainstream journalists bothered to check on those Iraq WMD claims or investigate the realities behind the 2008 financial collapse? How many politicians?
Trust is hard to earn and easy to squander. When it is lost it leaves a vacuum. If nobody is trusted the vacuum gets filled by whatever random nonsense sounds superficially good to someone.
To me the popularity of crazy populist demagogues is entirely explainable as a response to several large scale and very notable cases where our institutions have burned their credibility. If something isn't done to correct this and start re-earning trust I predict that this situation will only worsen and we'll be facing full-blown fascism shortly.
Censorship does not re-earn trust. In fact it does the opposite. Right now hordes of people out there are saying "see! Alex Jones must be onto something or why would they go to the trouble of banning him?!?" Microsoft's threat to ban Gab is the kind of PR money can't buy. I bet their traffic numbers will skyrocket.