The Return of the Archons
The starship Archon had visited ... so what? It was destroyed by Landru. It did not interfere with the culture. And your very statement that Kirk helped "a little" down plays what he did. He chose one side in an internal conflict, a side that at that time appeared to be losing, and changed the entire culture of a planet.
A century after the
Archon visited, a member of the resistance asked the
Enterprise crew if they were "Archons". That the name of the ship had persisted through word-of-mouth for a century says something. A culture like that would not have been ready for First Contact. Probable
Archon crew spilled all when incorporated into The Body. Plus the Landru computer used power beams to pull the ship out of orbit and crash it. An interstellar starship crashing on your planet is
definitely going to skew that world's "natural development". Never mind all the information divulged from brainwashed Starfleet personnel.
For all that any resistance movement has gains and losses, that one had persisted since Landru turned his computer on. I re-watched it not too long ago, and got the impression that this was one cell in a larger movement, although that cell -- being right at the heart of things -- was in a bad way. Even if it had been wiped out, others would carry on. And they had people right in Landru's facility by that point.
Given everything, yes the
Enterprise crew interfered, but there had already been cultural damage, and resistance movements have a tendency to not go away. History demonstrates the opposite. I am not being glib in saying that, on a cultural-evolution level, Kirk brought a resolution to things a little sooner than it might otherwise have, but that that conclusion was ultimately inevitable.
The Apple
You made a huge assumption here. You have no idea where Vaal came from nor did Kirk. He came in and once again changed an entire culture.
There was no evidence the indigenous people had ever had a level of technology to build such an artifact. Ergo, highly unlikely they inflicted that stasis on themselves a la Landru. More likely external influence like the Preservers of "The Paradise Syndrome", but more actively intrusive.
A Taste of Armageddon
Once again, you ignore a basic fact here. While Kirk did go in on Federation orders (specifically a higher ranking ambassador order) he still chose to interfere in a society because he decided he didn't like the way it was running it's war. So again, he made a major change that forced that society down a certain path.
The Gamesters of Triskelion
Kirk could have bet on his crews release but he went a step farther, he made a bet that included making a change to the larger society.
These are actually a whole other category. The Prime Directive is specifically about "less-developed" societies. Everything across the series (plural) paints a pointillist picture of single-planet, non-space-faring, don't-know-aliens-exist sorts of civilizations. Once they're on multiple planets and/or have interstellar/FTL capability and/or know there are other beings out there in the cosmos, the Prime Directive has been shown to matter less, or not at all. And where the question of meddling in internal affairs of other spacefaring civilizations is a point of discussion, it's governments they have treaties with, rather than a blanket prohibition like General Order Number One.
The only time I recall seeing the Prime Directive invoked in a multiplanet situation was in TNG's "Symbiosis", where Picard used a literalist interpretation to passively interfere in the Brekkian drug cartel and their victimization of their species' other planet. The Excalbians, the Melkot, the Triskelians, the Eminians and Vendikans, the Ekosians and Zeons, the First Federation, the Zetarians, the Edo, the Straleb and Atlec, and on and on and on... Our Heroes treat them more like peers than protectorates, even when the tech level or territorial scope are significantly disparate, one direction or the other.
It's why I question whether "The Return of the Archons" was ever even a Prime Directive matter. Yeah, they're on one planet, like the Edo, but the tech level was impressive. Why and how would a non-spacefaring world have equipment powerful enough to pull a starship out of orbit? In the episode itself, the locals they're talking to say that the planet had been more advanced, but when war threatened to destroy everything (a la Earth's WWIII, maybe? When we were already traveling interstellar?), Landru force-reset everything to a simpler time.
And "A Taste of Armageddon" remains a weird one. There are subtle and less-subtle contextual cues in the Captain's log slugs and in dialogue. The
Valiant visited there fifty years ago, ignoring a warning-away. Why did they ignore? How had the natives detected and communicated with the starship to stay out of their star system? If it was anything like the very next contact with the system, it was a code-710 transmission while the ship was still outside the system, via subspace radio. That indicates a planet with whom interstellar contact had already been established and codified, that there was a specific cited proviso they employed and that Kirk (and the
Valiant crew before, as their records indicated) recognized. Communications were probably initiated across interstellar distances sometime prior to the
Valiant's visit, though with no normalized diplomatic relations (Ambassador Fox's whole mission, after all).
After decades of knowing of the system, the Federation is hot to establish diplomatic relations "at any cost". That's not how one approaches a Prime Directive protectorate. The war has been going on for nearly five hundred years. Unclear how much of that has been the "virtual" war with computers. But I get a sense from the episode that the Federation's position is tacitly one of "this part of space is starting to fill up and get civilized, you can't stay isolated forever, if the Klingons or Romulans run across you, they'll just take over,
we actually want to get to know you." Probably why the
Valiant went in in defiance of the code-710, and definitely why the
Enterprise was ordered in.
