Eddie, remember Trek was based on the age of sail.
No, Trek was based on the age of American colonization (hence Rodenberry's "Wagon Train to the Stars" pitch and the treating of whole planets as simply larger-than-normal adventure towns). As such, Enterprise' mission was originally conceived as a group of professional explorers opening up space for Earth expansion on "the final frontier". The military nature of whatever organization the Enterprise belonged to wasn't really even a question (nor had they completely decided what kind
of organization that really was, e.g. UESPA vs. Space Central vs. Starfleet).
The series EVOLVED to a kind of begin to resemble the Age of Sail in TOS' third season, but was never really "Based on" that concept until Nicholas Meyer picked that premise and ran it for a touchdown in Wrath of Khan.
And, just because the Macarthur was a military exploration mission does not mean Starfleet has to follow Niven and Pournelle's lead on how it would operate.
I didn't say it necessarily should. I'm suggesting then "The Mote" never had any illusions about the human space force being anything but a full standing military organization, and therefore represents a kind of reference point to what "the military can also explore" would actually look like if applied properly.
Another (possibly better) point is the Earth Alliance in Babylon 5: nobody is mincing words about what Earthforce actually is, despite the fact that their largest and most awe-inspiring starships are specifically designed for exploration. Captain Sheridan is depicted as having occasionally performed exploration missions on the Agamemnon, and we later learn that Earth-Minbari War was primarily the result of a spectacular misunderstanding during an otherwise peaceful exploration mission into Minbari space. The Earth Alliance has detailed and extensive first contact protocols and devotes a fair amount of its resources to charting new worlds and contacting new civilizations as well. So here, too, we have a space military that seems to have a very large science/exploration budget, but has never pretended to be anything other than a standing military
and has never equivocated about their mission statement.
In summary: for all the characteristics people keep listing of modern militaries, the one thing they all possess -- the one thing Starfleet lacks -- is absolute clarity over the fact that they ARE the military. That there's even room for the question suggests everything we need to know.
This whole resistance to Starfleet being a military was an inane grafting in TNG, and I believe it grew out of hippie protests in the 70's calling soldiers babykillers. Roddenberry should have made the point that Starfleet was a better military than today's, instead of repudiating his own service and making ridiculous assertions that fly in the face of logic. And sadly, many who grew up on TNG instead of TOS have bought the idea.
Star Trek presented many strange ideas for many different reasons; the idea that an armed exploration service with an explicitly non-military charter could function as the primary peacekeeping force for an entire nation is NOT, in fact, the strangest thing they have ever asked us to believe.