Deplatforming fuels polarization, so one thing I would look at the PEW research study that shows how the center has collapsed, making it impossible for moderates to win elections: http://www.epsilontheory.com/things-fall-apart-pt-1/
More citations needed! This is a bare assertion that is not widely agreed upon. The polarization was getting worse long before the deplatforming trend started.
Since you started out the game, I'll add a bare assertion of my own. Constantly being bombarded with extremist views fuels polarization! Under that thesis, deplatforming actively works against polarization.
The moral of the story is that you can make almost any argument as long as you are allowed to rely on unproved premises.
The center collapsed because the establishment discredited itself in the 2000s: Iraq, the housing bubble, banks-before-people bailouts, etc. Now everyone is flailing around looking for alternatives. The hard right was first to the dance, but I see a lot of signs of growth on the hard left too.
I wonder if the hard left will get deplatformed too if the rhetoric starts sounding really extreme? They might, especially if there is a loud call for wealth redistribution.
But I could turn out to be wrong about that. We certainly live in interesting times.