Healthcare is free.
Starfleet certainly doesn't seem to charge for emergency services. But as a general societal policy, I was wondering if you pulled this from a particular episode?
Bottom line... Star Trek did a poor job of really explaining how the Federation credit system is supposed to work and how it would interface with extraterrestrial cultures.
We're given a window into why the Vulcans adopted their emotion control, they were destroying themselves as a group.
Warp drive, transporter, and other devices
receive at least a passing explanation. Sometimes composed of technobabble. In FC we saw the first (Human) warp flight. In Enterprise there was a episode about the first (Human) transporter use.
The show is completely lacking in explanation on the 22nd century's "the new economy," or what is meant by "the economy is different."
In the multiple series we get mentions of pay, accounts, bank, credits, buying, selling, etc. It sounds given the vocabulary used that their financial structure is a analogy of our own. If Picard's one time statement is the true picture of the future, what were all of those other Humans (and non-Humans) talking about?