Those gatekeeping functions were lessened after the violent Democratic national convention of '68 (where there was a clash between pro-war and anti-war factions) and primaries became a thing that actually mattered (in 68 Humphrey was selected by backroom insiders who did not participate in a single primary in that cycle, leading to public outcry). However, the gatekeeping effects persisted because of the control the parties still had over advertising channels and the media; that control fell apart post-2000, which setup the conditions that enabled a populist like Donald Trump to actually be elected to the presidency.
So it's not free speech that kept fascists out of power in the U.S., it's institutional gatekeeping (in the 30's and 40's).