Remember, the social Democrats sided with the Nazis over the socialists. They’ve done it every time they’ve been given the opportunity, and will continue to do so as many times as people fall for their shtick.
“The master's tools will never dismantle the master's house."
-Audre Lorde
If you heavily regulated companies, nationalize every major public service, place an upper cap to overall wealth for any one individual, eliminate inherited wealth and redirect all available resources to public education, health care, housing and UBI .... then democracy could exist in a capitalist system.
But chances are we'll more likely start WWIII with nuclear weapons than do any of that.
If you picture the political compass, where the y axis is how how democratic the society is(where the top is tyranny and the bottom is anarchy) and the x axis is how socialized it is (where the left is communism and the right is capitalism), OP claimed that ancap (the bottom right quadrant) doesn't exist, and that those who claim to be ancap tend to be authoritarian right instead. You argued that democracy could exist in a socialist (leftist) society. You are not disagreeing with OP, because what you described is not a capitalist (right leaning) society.