So the Federation has secret police, but you can't name them
No, what I'm saying is that the existence of a secret police is not a necessary feature of an oppressive, unfree state, it is instead a symptom of something completely different, a failing state. (FWIW, one of the secret police forces in Star Trek is Section 31, there are probably others.)
Again with the moving goalposts. First the Federation is terrible because it has secret police, now it's terrible because it has a different problem (but it still has secret police).
Incidentally, if it did have Secret Police they'd appear in more then a handful of episodes.
Which is roughly 1/700th of the universe, and much better odds then any capitalist system.
We aren't talking about "odds" here, we are talking about the nature of Federation government, and it seems to be a standard, run-of-the-mill government run by humans, the kind that we have millennia of experience and centuries of political theory for. (Furthermore, I dispute the "better odds" claim; historically, almost all socialist governments have failed, and those that haven't are totalitarian.)
Except, by your definition, most of Europe is governed by Socialists, and the most Socialist countries in Europe (the Northern European ones) are doing fine.
Capital goods are allocated by something we can't see off-screen which could very well be a market of some sort. Consumer goods are either obsolete (ie: cars) or provided by a replicator. Health is provided by some sort of socialized system which could be co-ops, Single Payer insurance, or an NHS clone. Education is totally laissez faire. Other then that there is no other then that because that economy works fine. With no economic problems, there's very little politics, and no reason for the government itself to do any of the things you're ascribing to it.
You are pretty much describing East Germany. The East German economy "worked fine" too, in that it provided housing, jobs, transportation, and health care to all citizens. It was also highly unfree, in that someone else told you where to live, what job to take, what housing you got, how much energy you could consume, and when you worked, based nominally on the state's assessment of your value to society and your ability to contribute.
You have yet to give any examples of someone telling a Federation citizen where to live, what job to take, or what housing to live in except in a military context. In fact canon is pretty clear there's no longer such a thing as a 'job' in the first place.
Which is quite telling, given your premise has apparently morphed into implying the Federation does that shit.
Its economy was performing poorly because, absent the usual market mechanisms, economic planners lacked the information to plan output or capital investments, workers and innovators lacked the information on what to work on. The numerous scarce resources (nice houses, rare art, desirable jobs, etc.) were awarded based on political connections and influence. To someone from a few centuries earlier, East Germany would have seemed a liberal, peaceful "post-scarcity" society, but compared to free market economies, it was an impoverished, oppressive shithole.
Look, we basically agree on the facts: humanity in Star Trek has eliminated money for personal transactions and gives everybody some kind of housing, education, health care, job, and resources for hobbies; particularly ambitious individuals--scientists, explorers, fighters--can join Starfleet and rise to power, fame, and (implicit) wealth within a military-style hierarchy. The difference between us is that you think that's a good outcome, whereas I recognize it for the oppressive and impoverished society that it is, because it really is little different from what the better socialist states were like in the 20th century.
So there's no poverty, there's so much stuff that any individual human has more consumer goods then they could possibly use, the ambitious can shine in Starfleet; and that's somehow a bad thing?