Spock: "Then the Prime Directive is in full force, Captain?"
I've alway found it interesting that Spock felt the necessity to ask Kirk this. It implies that there are circumstances when the Prime Directive isn't in force, or at least not in in full force.
Is it up to the commanding officer on the scene to decide?
And below "in full force," how many levels of "in partial force" are there?
And of course we realize that the Klingons would have gladly interferred with the planet's normal social development had they arrived first (or tried to anyway)
I'm not so sure. Not that the Klingon would mind doing so, but it's not my impression that the klingons were going to do that. They were there to establish a base of operations, not really to "take over" the planet. Unless there was a future effort to colonize the planet, I can easily see all the Klingons simply leaving after the war was over, or when the front moved elsewhere.
If the Organians were in fact primitives.
The Klingon choose that town because it was the largest community on the planet, and there was the old fortification (in case the locals rebelled). The town would provide the Klingons with existing structures so they wouldn't have to build any -- at least not right away. In time they might have wanted to build a minor starbase there.
After the Klingons were gone, how much "culture damage" would there really have been? At that technology level there would have been no planet wide communication. Outside of the immediate region, the Klingon presence would have been unknown. In the town seen, after a few generations it would have turned into local myth.