I think this stems from an idea of what socialism involves that even Marx would have dismissed as irrelevant and utopian.
In fact, Marx railed relentlessly against the notion of socialism/communism ending all inequality. One of the more famous cases of that being in the Critique of the Gotha Programme, where he criticises what became the SPD for even talking about "equality" without defining it precisely. This is where the (Bolshevik) distinction between socialism and communism comes from, though Marx talked about the "lower" and "higher" stages of communism, and argued that the lower would explicitly retain a lot of inequality, and that anything else would be unfair because people have different needs, and so inequality is according to Marx a pre-requisite for a fair society.
The point he made was that the goal was not to give everyone everything for free - instead he explicitly pointed to a then well established slogan: "from each according to ability, to each according to their need". The point being that his expectation - one he stated explicitly in the Critique - was that there would very much still be an exchange where peoples access to that seemingly endless material wealth is contingent on their participation in doing their bit keeping society running. He did not expect a true post-scarcity society, but one that met sufficient needs to eradicate class struggle, but which at the same time still had a need for people to work.
In that respect, the Federation strongly imply it goes further than Marx, in work being implied to be fully voluntary, and I do think we can agree there are plenty of unaddressed issues there. Though I think it's not that substantial, in that there's are many other ways of providing rewards than through material wealth, and there's nothing incompatible with socialist thinking in that.
My point, though, is that you have socialism and communism long before you get to that stage. Eradicate class struggle by eradicating the ability of anyone to monopolise production, and you have communism, irrespective of the specific details of how allocation of resources is arranged. Which is why you'll find communist ideologies that advocate for free market models and the like as the best means of making such a system work.
Will there still be exchanges of value? Sure. But those exchanges will necessarily look very different when everyone has the ability to access sufficient material wealth to be able to walk away from any transaction without fear of starvation or not having anywhere to live. That freedom is the point, not some notion of absolute equality in all things or entirely eradicating money.
And that is why I'm arguing that any sufficiently utopian/post-scarcity society will seem socialist. Not because there's no exchange of value at the margins, but because it's a small enough part of the lives of the typical person that being constrained by resources rarely comes up.
TNG was definitely the peak of this. The crew of the Enterprise in that show don't turn on each other, make mistakes or do dumb stuff. This was an explicit rule by Roddenberry: in his utopia Federation officials never fought each other. The writers called it "Roddenberry's Box" because it was such a limiting rule, and the Box is why so many episodes feature mind-controlling aliens of various kinds.
Any post-scarcity society will look like communism/anarchism unless it is intentionally keeping part of its population poor for no good reason
I don't think this is true, see my other comments on this thread. Trek-style post scarcity where material things are non-scarce still doesn't cover anything non-replicable like people's time and attention, and by implication, service industries.
Until there is sci-fi that explains how a society eliminates scarcity of non-physical things like status, power and attention, the future will remain capitalist by default.