Of course, Kirk & Spock preceded Aubrey & Maturin, so if anything, O’Brian borrowed/stole from Roddenberry.
The naval paradigm led to an amusing remark in one of our tabletop science fiction games. During character generation, we had to roll dice to see if our characters had been in (just mustered out of) the Galactic Navy…if they failed the roll, there was a roll to see if they’d been in the Sector Navy…and if they failed that roll, a roll to see if they’d been in the Planetary Navy.
I asked, “what if we fail THAT roll?”
The game master replied disdainfully, “Then you’re coming from the wet navy.”
Star Trek’s metaphor is undeniably ‘nautical’ in nature, as many posters have pointed out. In terms of “does that make sense”; it would seem that it does, once you are looking at a fully evolved ‘star fleet’ entity. If we were to postulate the path forward from current-day reality to something like Star Trek’s star fleet, though, I don’t think you could get there directly from the current naval services.
Consider the example of the US Air Force. Its origin was as a branch of the US Army (greatly simplified, see here for the full story) before some name changes and bureaucratic reorganizations eventually led to the creation of a new armed service. In our present reality in the USA, what government agencies are most involved in space exploration? NASA obviously, the USAF has some experience, and the Navy has their ballistic missiles as well. But current space vehicles are much closer to aircraft than they are to submarines, even though submarines are the closer match to Star Trek’s ships.
As far as a military space service (let’s leave aside the debate as to whether Star Fleet is military or not!), I think it would have to evolve in the shorter term from the USAF. But there is already activity from the other entities and many other groups have satellites in orbit (consider surveillance satellites). Then there is also the example of naval aviation: Why doesn’t the Air Force simply cooperate with the Navy to operate from air craft carriers? The Navy and Air Force have different missions and requirements, so despite the fact that they both operate aircraft, their aviation branches are separate. So, my opinion is that the path toward Star Fleet would start with the USAF and NASA. Then as the space vehicles get larger, and with more military applications, you would see joint service operations. Eventually, there would be a new service created that would roll up some elements of the USAF and Navy into a new entity.
In fact, we have already had a US Space Command, which grew out of the USAF. That later merged with US Strategic Command (itself successor to Strategic Air Command), which is a Unified Combat Command that “employs more than 2,700 people, representing all four services, including DoD civilians and contractors”. USSTRATCOM is lead by a USAF General and has an insignia very much like the SAC insignia. So that seems to be exactly the path we are going down, even though there will likely never be something like a Star Fleet in reality.
So towel off, hoser!
Kirk even says in “Tomorrow is Yesterday” that Starfleet is a “combined service.” Franz Joseph, in his 1975 ST Technical Manual, suggested that this was from the consolidation of several founding races’ space navies in the earliest days of the Federation.
Traveller.
LOL. I suspect O’Brian had more of an eye on Nelson’s late 18th century navy than he did on 1960s Star Trek. Being resident in either Ireland or England, I’d also be very surprised if O’Brian saw Star Trek before the 70s.
Also, you might think there’s a giveaway at the start of each episode "These are the v … "
Oh, I was in no way seriously suggesting that there was a connection. But I did once have a discussion with someone who was convinced that Kirk & Spock were based on Aubrey & Maturin, until I pointed out the dates to him.
Of course it’s navy. The post the OP references says space isn’t an ocean…well I’ve got a trope that says Space is an ocean. Suck on that!
It’s and organization the likes of which don’t currently exist where its three main functions are Defense, Exploration and Scientific Research and all are equally important.
The Military aspects get most of the attention because that is the most entertaining for us to watch and it uses a Martial organizational structure.
Starfleet is not posited on any 20th century military structure, it is posited on 16th to 19th century Navy. The analogy is clearly there, with a Captain serving not only as the senior officer of the vessel, but often the senior government representative to a new region. Ships were large vessels outfitted for lengthy journeys serving independent missions, rather to colonies or exploration of new regions and contact with new indiginous peoples.
This is a longstanding metaphor used in science fiction. Roddenberry was not charting new territory here.
From the perspective when these ideas were being generated, expanding the navy into space exploration was the natural extension, not the Army or Air Force or Marines.
As far as projecting the future from now and trying to chart a path, who knows? It is very likely to be a new agency formed from elements of a lot of sources. There may be a new structure. On the other hand, if space actually goes to the detail they represent in Star Trek with Starfleet, the return to a Naval structure makes a lot of sense.
The kinds of movements and orientations and such are irrelevant. The technology is going to drive the type of vessels and the means of movement and the interactions between vessels. Just because modern TV/movie writers find it easier to use 2-D wet navy tactics and gravitational field atmospheric flying craft tactics more easy to think about, plot around, and convey to a modern audience has no bearing on how the tactics and strategy will actually unfold. The hierarchical structure of the organization is independent from the physical motion of the vehicles involved.
Just like the modern Navy has adapted to Carrier format and incorporated airplanes in their operations. The military structure will adopt new techniques and tools as they become necessary.
As far as Enterprise was concerned, the MAKOs could be seen as the direct corrolary to Marines - soldiers deployed on naval vessels to supply security and ground deployment activities. The naval crew operated the ships and the cannons on the ships, the marines carried the rifles and did landing assaults and such. Naval crew would perform boarding actions and repel boarders, with or without marines.
Nitpick: MACOs: Military Assault Command Operations | Memory Alpha | Fandom
When it’s called Starfleet doesn’t that make it kind of obvious? A fleet is a group of ships.
I would add Diplomacy to their core mission statement.
Well, Balance of Terror was, because it was based in large part on The Enemy Below (which everyone should see - it is a great movie.) Later battles were far more like battleships pounding away at each other from long distances, before the time of aircraft carriers.
But it is definitely navy - in fact Kirk can even marry people, and at the beginning of Balance of Terror specifically mentions that this ability comes with being a ship captain.
Based on their ranks(Ensign, Chief Petty Officer, Lt. Commander, Commander, Commodore, and Admiral, they’re based on the Navy, not the Air Force.
Treating the battle space as 2D or 3D or even 2 1/2D would largely depend on the presence and locations of gravity wells. Tactics in orbit around a planet would differ greatly than those used in interstellar space. Combat in solar systems would probably be a hybrid of the two with its own problems to deal with as well.
Well-armed diplomacy, at that. It sometimes helps. 
That’s the best kind.