It isn’t just combat that creates the analogy. Think of all the tasks and missions navies have performed in their long histories. This includes exploration & discovery, colonization, first contact with new cultures and closed cultures (e.g. Japan in 1871), opening and protecting trade routes, fighting piracy, and missions of ad hoc diplomacy. Large, multi-service expeditionary forces are usually commanded by the senior Naval officer.
Countries with deep naval history have a long institutional memory, codes of conduct, processes, and precedence for all these situations. Historically, and still today in submarines, Naval officers must be able to handle situations and make decisions of great import independent of conferring with higher command. Think of the exploration of Captain Cook in the 18th century as he discovered new lands. He essentially acted not only as a military officer, keeping discipline and readiness of his crew, but as a diplomat and social scientist, discovering new cultures and kingdoms and negotiating trade treaties, along with mapping new discoveries and documenting the new cultures.
On the technical front, the maintenance, upkeep, and operation of a space cruiser is definitely more akin to what current navies do, as opposed to the air force. Think of all the functions to be maintained: water treatment, air treatment, nuclear and oil based power systems, large propulsion systems, hydraulics and pneumatics on a massive scale, large scale mechanical systems, ship damage control systems and processes, supply and feeding of large crews cut off for long periods of time from supply stations. The air force does none of these and has no history of doing any of these things.