So, Gene, a Hippie on the left, had a dream vision of the future. Laudable, certainly. Peace, brotherhood, and many evils of society worked out.
Except that he wasn't really. He was what's rapidly becoming an extinct breed of Republican... the Nixonian strain which was highly conservative on many social issues, but progressive on others such as environment and a restraint on greed. If you look closely at TOS, the show clearly is dismissive of the counter culture movements of the day, and was strongly supportive of American involvement in IndoChina. Roddenberry's ideals were highly drawn from the white picket fence culture of the 50's... and like many of his generation were put off the 60's radicals. And Roddenberry's TOS... clearly used money in all it's forms.
Keep in mind that by the time TOS is on the air, Roddenberry had already been eased out of being the big decider after the nearly fatal disaster of the production of the first Trek movie. He remained the titular patriarch of the franchise, but was increasingly relegated to a figurehead role. The money-free ideal of Picard's World is a creation of later minds.
Correction on that that should have been TNG instead of TOS in the second paragraph