What makes you think the Akira or Sovereign classes are warships?
Behind the scenes sources for the Akira, IIRC the guy who designed it said it's essentially the Starfleet version of the an aircraft carrier. For the Sovereign, I'm going with what the say in the novels, non canon though they may be. It was even a plot point in a recent one. Still, the Akira was only seen in combat situations.
The Defiant and Prometheus were presented as one off prototypes until the Defiant was retconned into a class in the final episodes of DS9 so they could reuse the sets and stock shots.
Actually, no. Message in a Bottle in Voyager's 4th season (which is concurrent with DS9's sixth) showed two Defiant class ships sent to retake the Prometheus. Also, in DS9's sixth season there was the Defiant class Valiant, though that admittedly was an excuse to reuse sets. Memory Alpha also claims there were other Defiants at the end of DS9 season 5 in A Call to Arms. I've never spotted them, though I do remember it being mentioned in the old Star Trek Communicator magazine.
If Starfleet were meant to be a military, why do the writers time and again go out of their way to state that it isn't? [snip] The people behind Star Trek clearly do not want us to consider Starfleet to be a military organization.
Nick Meyer and Harve Bennett definitely thought of Starfleet as a military. Nick Meyer was surprised to hear Roddenberry claim otherwise, and Harve Bennett lost his shit and accused Roddenberry of saying anything to discredit them. In the later shows, Ron Moore claims he sees Starfleet as a military, and has complained that the claims that it isn't military are just examples of Roddenberry's "godhood" being an overbearing presence to the franchise, even years after his death.
But in TOS Starfleet clearly is intended to be a military. Everyone writing the episodes based Starfleet on their own military experiences, James Doohan and DeForrest Kelley definitely drew on their military experiences for their portrayals. There are reports that Roddenberry himself even complained the third season did not accurately reflect military lifestyle. The Starfleet of TOS was clearly military, and if you told anyone in the 60s that it wasn't they'd likely be confused and wonder what you were talking about. Hell, Star Trek is based in part on Forbidden Planet, and that was definitely about a space military exploring the galaxy.
The "Starfleet isn't a military" line has the following origins:
-The military losing popularity in the 1970s due to Vietnam, which likely is why TMP cut back on the military parallels.
-Roddenberry pissed off over losing control of the movies after TMP and wanting to discredit Bennett and Meyer.
-By TNG Roddenberry himself had developed an unexplained hatred of the military, as evidenced by him banning Diane Carey from writing anymore Trek novels after she dedicated one to a friend who had recently been killed in military service. A ban which wasn't lifted until after Roddenberry died.
Simply put, the idea that Starfleet isn't military is revisionism, plain and simple. Unfortunately it has been blown way out of proportion to the point that it has become a holy commandment the franchise is obligated to uphold, despite the fact that the franchise continues to depict Starfleet as military-like anyway.