I'm not sure I follow. To me, recent polarization is a product of echoChamber * confirmationBias. e.g. (1) I subscribe to a trustworthy information outlet on $PLATFORM that reflects my beliefs. (2) I am recommended related untrusted content to increase my engagement with $PLATFORM. (3) I do not verify the related content because it reflects what I already believe. Rinse, cycle, repeat. Forcing voters to "shut up" means only allowing information to be shared by trustworthy sources. Over time I suspect that decreases polarization, at the expense of free speech.
Voters are not forced to shut up, though. A big portion of them are just mad that a) other people don't want to listen to them or b) that they're asked to express themselves without being extremely rude or aggressive.