There was this single agent from "Federation Security", yes - delivering McCoy straight to a Starfleet gaol!
If a United States Navy Commander were delivered to Quantico Marine Corps Brig
, does that preclude him from having been arrested by the Federal Bureau of Investigation?
The detention agency doesn't imply anything about the arresting agency.
If anything, I'd count that as a further strike against the existence of a civilian police force in the Federation.
a civilian police agency engaging in policing actions is a strike against their existence?
Strange world you live in.
UFP is not an unified nation state but an alliance of different worlds.
That may have been the original intent, but that changed over time
. And even at the start, the Federation was never quite just an alliance -- alliances don't get their own dedicated military like Starfleet. There's no such thing as the United Nations Army, after all.
Oh, and NATO and UN forces kinda operate the way I suggested, and they seem to work just fine.
NATO is just a puppet of the United States, and the United Nations is the puppet of the P-5. Neither one is capable of the kinds of sovereign political actions we have seen the Federation engage in.
The word you are looking for is "sovereign state,"
A nation-state is a sovereign state explicitly designed to encompass the territory and citizenry of a nation -- and no, "nation" is not a synonym for "country" or "sovereign state." A nation
is actually a large group of people sharing a common culture, language, and imagined history.
Thus, a nation-state
is when a sovereign state is designed for a nation -- the French Republic for the French nation; the Kingdom of Norway for the Norwegian nation; etc. Some nations have no states -- the Kurdish nation is quite real but there is no Republic of Kurdistan. And some states encompass multiple nations -- the United Kingdom of Great Britain and Northern Ireland compasses the English, Scottish, Welsh, and (part of) Irish nations. Etc.
The Federation is clearly a multinational sovereign state.