Free speech for all political factions on major public forums is the cooperate-cooperate quadrant of the prisoner's dilemma. If forums controlled by the blue faction defect and start censoring the red faction, the red faction needs to threaten to retaliate in order to scare the blue faction into cooperating again. It's simple tit-for-tat. This is game theory 101.

Surely, it's clear here that having the actual head of the US government threatening to shut down private companies

The United States President has neither the authority nor power to start censoring Twitter on his own. Right now, Jack Dorsey has far more power over allowed public speech in America than Donald Trump.