But aren't Khan and Marcus' views subjective? Given that, as you said, Marcus wanted a "proper military", and that Starfleet is certainly the governmental organization that would have to deal with the Klingons, doesn't that tell us that they are indeed a military organization, just one that is more varied in purpose and perhaps overstocked with scientists?
Marcus' point in reviving Khan was to ENHANCE Starfleet's combat repertoire. He felt, rightly or wrongly, that Starfleet was not martially prepared to take on the Klingons and win. Hence his "thawing" of Khan and the creation of the Vengance
, which is the largest Federation ship yet seen in the series.
Just because a military force isn't experienced doesn't make it any less of a military. Lets look at the combat record of Starfleet in the new universe.
Starfleet gets curb stomped by a future Romulan spacecraft. 6 billion dead, an entire planet w/ attendant resources and culture savagely destroyed, and half of Earth's fleet is lost with all hands. To put that in modern perspective, that would be akin to half of the US Navy being wiped out by ONE ship.
Now, decades later, there's a good chance of a for-real war. Considering Starfleet got its hiney kicked in the last battle, we really can't blame Admiral Marcus for having a crisis of confidence in the fleet. A real-life historical analogue would be the US Military in the early years of WWII. Many of our ships, aircraft, and infantry tactics were severely out of date compared to the modernized forces of the Axis. That didn't mean we didn't have a military, just one without modern battle experience.