I would not call any incarnation of the Federation in Star Trek "moneyless". The currency you can never rid yourself of is energy. No matter how much "free" energy an individual is allotted, you can always imagine scenarios that would scale up and require even more energy. So, you have enough energy for your Winnebago to reach warp speed. But can you terraform a whole planet? You will reach a point where infinite desire is curbed by limited throughput of energy. Sentients will always place "value" on energy. Energy will be traded based on this perceived value. Congratulations, you have money again. There might not be scarcity for daily existence, but there's still not enough to fulfill all dreams.
I imagine the technology in Star Trek would make it so nearly all pregnancies are by mutual volition. People would bio-engineer their own flesh so everyone is asthetically pleasing and move like Jackie Chan. The nervous system would be redesigned from the bottom-up so one could experience mental and physical pleasure to new heights and for prolonged durations. Intertwining genitals for fun would be a nostalgic novelty at best.
Long story short: providers would be rarer than a trained passenger pigeon.
FWIW, episode 5 the short-lived HBO series
Spicy City touched on this. Old-fashioned prostitutes had a hard time eeking a living in a world deluged with sex virtual reality machines devoid of STDs. Most wives didn't consider the machines' use cheating.
