Jake wasn't the only one, Picard stated it numerous times too.
Picard only said it once. In
First Contact he said something like, we're not payed, we do it to improve ourselves, which contradicts with Crusher's and Janeways actions and story. He also said, "the Econonicms of the future are very different," when a 21st century business man asked to see his accounts portfolio. Janeway did say in one episode, "We don't use money," while holding a handful of alien coins, which contradicts her Vulcan price gouging story, so I take it to mean money = physical currency. Back to Picard, I suggested that Starfleet personnel may very well not be payed but have access to a shipboard account, which Crusher mentioned, and that everyone can take from as they please rather than it being a personal account funded by payroll. Alternatively, Picard's statement was hyperbole, they are payed, but he believes everyone, or just himself joins Starfleet for the benefits to self improvement. He actually didn't join for self improvement, he just wanted to explore.
Nowadays we have a monetary system that is just too abstract to comprehend, money is pulled out of peoples asses if I may be so blunt.
Gold has no more innate value than does money based on the economic strength the nation. While gold constantly inflates, paper money allows for additional controls.
This economy thrives on need over availability hence the poverty in it. As long as you have money and constant positive population growth you cannot have a lack of poverty.
Money regulates limited resources, and wealth has been expanding faster than population grow, otherwise we would all be serfs. And, I don't see Russia's and Japan's negative population growth helping. Poverty is a relative term that expands as the wealth of a society grows. Civilized poverty once meant having a loincloth and eating only the berries passersby might drop in you bowl. Modern poverty is more like pre-19th century broke landed gentry.
The thing I would mostly object to Star Trek about all this is that you have positive population growth shown without money and sustainability. These two don't flow together well. You can have one of the two, not both. Any advanced civilization in order to have sustainability needs to have a population that has zero or negative population growth and a population size who's needs don't exceed the availability of resources known to them.
Their population can never exceed the resource base, the solar system has so much raw resources that it would take 100,000,000 years to consume all of it at our current population, and that's with using each unit of material once rather than using it over and over. If we go by
First Contact, Earth only has a population of 9 billion in Star Trek, even if Mars has that population too, which is unlikely, then it's not enough to seriously cut into that number. First, they use hydrogen for power, the most abundant source of energy in the universe, second they seem to be able to flip hydrogen atoms to anti-hydrogen at nearly no energy cost, thirdly, replicators equal perfect recycling at only an energy cost and no material loss in deconstruction.
On the thing about human spirit, if a human doesn't learn from his own kind, he won't be mentally human, but will take on the characteristics of the species amongst who he grows up. Human-like apes don't have that issue since their young don't depend on their grown ups to learn from.
That's because humans learn from society, and they'll take up whatever there is available. At the risk of oversimplifying dogs, if all there is is sniffing butts to say hello and growling at strangers, then that's what the kid will do. Humans depend on observation and context for a significant amount of how we act. Cultures are just tool sets.
On the contrary, it's similar for apes. Apes raised by humans learn human and human like skills. Where one set of apes may learn from their mothers how to collect termites from a log with a stick, and the mother will actively teach the child, ones raised from humans have learned how to get in a boat and paddle around with their hands, and that they can put nails into wood with a hammer, they are also able to (innately) apply abstract skills without training, such as being shown how to hit two blocks of wood together to make a sound, then figuring out on their own they can do the same thing with cymbals. The effects simply aren't as wide ranging because their capacity to learn is limited in various ways in comparison to humans. For one thing, despite having something like language they have no mental structure for being curious about people, nor wanting to talk about themselves, if memory serves. Their ability to comprehend reality is also at a lower level as shown with tests such as treating rocks as pets and dead birds as sand paper, and having the ape choose the weirdest thing. They end up failing the tests at a level where a six year old would succeed.
Lastly, never ever mix the word communism with what happened in the Soviet Union or elsewhere where that was used. They don't deserve being called like that. Communism in it's core form was never used anywhere. If you regard that sentence of mine as backwards, that only shows that you are unable to think out of the box on the matter and purely view the ordeal from a strict point of view of a person who was raised in the materialist view, that's the only reason why your opinion on that matter is biased. On this, you fail at seeing what science fiction wants to tell us among other things. Economics as we know it today is an outdated system, period.
To argue communist countries weren't communist is to argue that any system that doesn't work as desired wasn't that system. Communism is outlined in very general terms with no explanation of how to achieve the stated conditions for transition (other than spontaneous public revolution, although he probably meant that he only specifies that a revolution take place, not if it is lead) and in places where those goals have been achieved some, fortunately not all, have required horrible means, and if they didn't use horrible means for achievement some have had undesirable to horrible results, again not all. It also draws odd conclusions as to what those goals will lead to.
You're putting words in the mouth of the science fiction in question. No where in Star Trek do they say they dropped the ideas of materialism then became non-materialist, in that order. I called your comment backwards because I think it gets the order of requirement and result backwards. If you read my first post in this thread you will see that I have a clear idea of how Earth and the Federation economy can exist. However, to achieve that society the technology of replicators and fully automated fully flexible factories have to be invented, more than that all labor must be easy and not much more difficult than managing machines. Once all goods are cheaper than dirt to manufacture and have little human involvement the importance of possessions will naturally decline because proliferation of possessions is no longer an indicator of wealth.
However, there remains the problems that someone must design the products and the fact that much of the worth of an item has always revolved around the perception of desirability. For instance, the iPod produces its own desire in people, it's the ultimate product achievement.

A better example is the tulip trade in the 17th century. Value of tulip bulbs grew wildly out of proportion with rational value, then collapse just as with the housing market today. The reason for that is simple, when people see people buying stuff and the value going up a bit they buy the stuff too hoping to get rich. This has a avalanche effect where the price increases further thanks to the new buyers who really have no interest in the product for its own sake, this draws new buyers, which inflates price, draws new buyers, inflates price, and so on. Eventually and rather suddenly, rationality strikes like a hammer once the price reaches a height that is too absurd. Suddenly no one can sell the product, and you get a reverse avalanche going down and people gradually realize they need to bail out. Non-bubble based desirability building involve things such as limited releases of easily mass produced items, and hand crafting. Star Trek has the equivalent of limited release, as any item that is hand crafted (Chateau de Picard wine and Sisko's cooking) is itself a one of a kind item. Because, no matter how similarly you make two vases of the same design, if they are made by hand they are not actually the same when almost all items can be copied down to an atomically perfect level using replicators. As I mentioned in past posting, if Earthly government wanted they could ration those luxuries by way of waiting lists or credits specifically for luxury items. It could work simply because those who work those particular jobs were shown to do so out of love for the job itself and not out of any necessity to support themselves. In reality, their jobs may have been hobbies.
The reason I said your comment is backwards is because perceived value will not decline just because people want it to decline, there has to be a reason for the decline. Replication, and other technologies turning all labor into highly skilled professions fits for that requirement, where as communes, communist countries, and other such experimental communities show us just wanting it does not make it work as desired.