The problem is that if everyone's needs were taken care of, then no one would work.
Except that plenty of people today work for no pay, or in jobs where they have to pay for the privilege of working. Typically, these are people whose needs are adequately but not exuberantly taken care of, and they work in the shittiest jobs imaginable (say, rubbing oil off dying birds).
The only real question is, does the UFP have enough of these volunteers to take care of the entire population? We don't know what the dependency ratio in the Trek 24th century will be. Today, it's about forty to fifty percent in those advanced western nations where high tech combines with high demand for comfort, and where charity work is very common (and where one simply counts everybody of working age as working, and everybody of non-working age as being a dependent). But in Trek, it could be more like 99.99999%, with a tiny fraction of the population taking care of the rest. With sufficient technology, you'd only need one farmer and one repairman and one logistics coordinator to feed a million people, etc.
For the necessary but unenticing jobs, you could easily draft volunteers who'd get bored after two days, at which point you'd draft new volunteers. Such jobs wouldn't require training, after all, and advanced information and communications technology would make the drafting trivially easy and extremely efficient. For those jobs that require advanced training, you'd just as easily find highly motivated hobbyists who'd eagerly dedicate their lives to, say, performing surgery for free.
Once you have the workforce, you can move the goods without having to care about moving the money. That is, some sort of "money" is obviously moving whenever goods are - books are being kept and so forth - but the people doing the work don't need to see any of that money, ever. What'd they do with it, if there are no shops that would accept it, no people willing to do anything they don't already want to do no matter how much money you push in their direction?
Economies like that are commonplace here on Earth. They are of fairly small scale, and work within a larger capitalist economy - but only because larger economies involve things beyond labor, things calling for bookkeeping. There's no inherent need to involve money in the organizing of labor.
Timo Saloniemi