I think you've missed the ultimate significance of the replicator for their economy. It's true that Star Trek is a kind of space communism, while North Korea is very obviously an earth-bound communism. What you're missing, though, is the fundamental difference between the two: Star Trek has universal abundance, while North Korea is poor as shit. (I'll premise this by saying that I know the original series only a bit; my view of Star Trek is MUCH more about The Next Generation series.)

If replicators provide whatever people want or need at any given moment, then what you have is universal abundance. Supply and demand become meaningless because scarcity is effectively gone. In that situation, material objects themselves would have far less significance than they do now. Socio-economic class would disappear; there would be no reason to accumulate more material wealth than others, because in theory everyone could just replicate whatever they want. There's no need to have a big house, expensive clothing (nothing would have prices!), fancy food--except in so far as you wanted to have more space in your house, clothing that had certain use or aesthetic qualities, or food with certain flavors or nutritional value. And yes, if you have replicators to do all your work for you, then there is no need to work--or, at least, there's no need for a wage labor market, since there is no scarcity of labor that can be met by trading material objects or exchange value for people's time. There's no incentive to work, and no incentive to employ people.

If we accept that premise of the Star Trek universe, then we also need to adjust our expectations and view of things like what humans actually do with their time. What would be meaningful, desirable, "good" in a universe with abundance? Well, it would be whatever people chose to do at any given moment. Since replicators don't appear capable of making the complex decisions and value judgments required for space exploration, interstellar diplomacy, or art (notice how any chance they get to show leisure time, people are painting, or doing other forms of creative activity?), then humans are free to pursue those. Indeed, it is the pursuit of knowledge itself, or of artistic achievement, or interpersonal relationships that seem to drive human activity in this universe--and that makes perfect sense. If people no longer need to work for wages or basic material survival, then why not set up institutions to allow people to pursue personal happiness and social harmony? What reason could there be for NOT doing that?

This, though, is why you're totally wrong about the comparison to North Korea. It's true enough that money is not particularly important in either the Star Trek universe or the North Korean economy. But while Star Trek has solved the problem of scarcity, North Korea manifestly has NOT. So the motivations, nature, and effects of doing without a market economy are about as different as you can possibly get. I agree that there's a superficial similarity, but all it is is superficial.

Let me acknowledge that there's a fundamental contradiction, or perhaps a misrepresentation or ambiguity, in how the Star Trek universe's economy works. On the one hand, you have replicators, which apparently provide universal abundance. On the other hand, everywhere you go, you see commerce, and various kinds of work: farming, mining, and the like. These ARE contradictory, because if every society has replicators, then in theory each society would have all the things it could possibly want, and there would be no scarcities of items to create demand. Certainly there'd be no reason to transport goods from one planet to another, since replicators in each place could just produce whatever you wanted. So, the Star Trek economy is an awkward mixture of things that make sense and things that don't.

Finally, you dropped some casual anti-semitism in your post: "the Ferengi, the space Jews, were greedy and only cared about money." You moan at the end about people believing "the meme," whatever that's supposed to mean; the meme of Jews as uniquely money-grubbing is one of the oldest memes of European society. So you've apparently bought that one. And, since casual anti-semitism is based on bullshit, you can take that and shove it up your ass. Don't be a prick needlessly.