The only thing missing from Trek is ridiculous start-up check lists. We only see it once in TOS when they’re cold starting the warp engines.
Yeah, supposedly they’re not required because…computers…something, something. But as seen in Star Trek (2009) when Enterprise misses the slaughter over Vulcan, they DO need checklists.
While Picard has StarFleet breathing down his neck wherever he is. The TOS Writers’ guide relates Kirk to Hornblower and the British Navy, out of touch for long periods. Balance of Terror did this well, with him asking for orders and getting back “do what you think is best” after the action was all over.
I don’t think you need Starfleet to be a military organization for this question to matter. We do know it borrows its structure from the military, with the ranks and chains of command. Any non-military status seems to refer to goals, rather than structure.
(I personally think of it as a PR move in universe. They don’t call themselves a military organization because fighting is not their primary goal.)
First off, all of the Star Trek Captains were aviators.
Kirk was a Navy fighter pilot/jet jockey. He won the Top Gun competition by sneaking out to his jet the night before and loading live ammo, successfully arguing that while standing orders prevented the ground crew from doing that, nothing stated that the plane commander couldn’t. (Afterward he seduced the Admiral’s daughter.)
Picard flew Air Force transports. Riker was a Radar Intercept Officer (RIO)/a backseater in a fighter/bomber.
Sisko was a Marine helicopter pilot who transitioned to Ospreys (a little bit of everything).
Chief O’Brien was the crusty Army warrant officer from the days before a college degree was required to fly.
Odowas the aircraft.
Growing up as a Marine Brat and doing time in the Navy (4 active, 8 Reserve), I’d say Picard - characters/unique personalities don’t rise to command positions these days.
I have limited experience with real-world military officers, but I do know that if someone told me I was going to serve in a military force and that I had to choose a Star Trek captain to be my CO, I would go with Picard every time. For one thing, his skills as a diplomat are very nearly superhuman, which gives me the best chance of not actually having to fight anyone.