You know that money was invented because barter like you described was clumsy and impractical. Now we are to believe that the oh-so-progressive 24th century UFP returned to this primitive system - why? Because materialism is the new sin?
Unconvincing.
To you perhaps, but as 'clumsy and impractical' it may be, it's easier for the Feds to barter with races because there isn't any evidence of a 'Galactic based currency'.
In any event ... the barter system (as opposed to the currency based one) was seen on-screen in numerous occasions and is much more productive because goods are directly transferred, and not 'money'.
In the real world, theoretically speaking, money was invented to also regulate resource use ... and it's used for anything BUT that when I see just what the system in question brought (stagnation being one of them as well).
It has been stated that they don't use money, but not how this is supposed to work on a practical, day-to-day level. And I still don't see how it could work, at least not universally. And why it should be plausible, just because the characters say it is so.
Yes, because what the characters say is practically the only thing we can go on with for one thing.
For the other, the UFP is an interstellar organization and the show is supposed to be set hundreds of years into the future, and Roddenberry's intent was that capitalism did NOT exist.
The bit 'we don't use money' which was confirmed on numerous occasions is a clear enough statement to me.
And how can those two systems coexist within the same organisation?
As I said ... internally, UFP doesn't use currency (other posters already provided ample amount of evidence to support a premise for a moneyless society which would work within Trek and on-screen evidence to support the premise has been stated ... if loosely).
I'm only saying that the UFP as a governing body (or SF officers) would use currency based system (by producing a necessary amount of the said currency) with races that still use it and will not accept simple resource exchange.
Janeway had to do it for example in the episode where Torres's violent thought was extracted and she was prosecuted as a result.
Janeway said she was not used to working with currency for one thing, though they had to use it because the race in question did.
On numerous occasions though, we saw trading happening between the UFP and organizations/individuals/whatnot that were not part of it.
This transaction utilized a barter type system which stated that an amount of x resources is to be exchanged with x amount of other resources (in Voyager's case when they were about to get the Isokinetic cannon ... it was 114 Isolinear chips for the cannon itself, with another 5 for Kovin to supervise the installation of the cannon in question - Janeway clearly never utilized currency, but exchanged a generous supply of Isolinear chips for 1 cannon).