And Roddenberry's cosmos was largely a military realm, where of necessity business enterprises took a back seat to military requirements. We don't know what earth or its neighbors looked like in Roddenberry's 23rd century. So far as I know, we only see the lightly settled frontier planets and the ships that police them. So it's only natural that private firms and individual enterprise don't play a major role there.
Much of the ideology behind Star Trek (or The Twilight Zone) was tepid Sixties liberalism -- civil rights, civil liberties, international organizations, collective security. If there was some deeper hostility to private property involved, it's hard to separate out the real political edge from the demands of creating a fantasy world -- one that was very different from Earth ca.1966 AD, one that resembled the conceptions people had of outer space at the time, and one that had enough space for adventure and the astounding.
Plato or St. Thomas More or Tommaso Campanella wasn't necessarily advocating putting socialism in practice, when they wrote their utopias. There was a certain amount of fantasy, of whimsy, of allegory involved. Roddenberry was -- well, first of all he wasn't any Plato or More -- but he was more political than they were. Still, there was enough of the fantastic and other worldly in his shows that I don't think you can say that he was sketching an attainable blueprint for a socialist future. Sometimes, utopian fiction is a compensation for the unattainability of dreams, rather than an incitement to realize them.
RIP William Windom.