First, Starfleet personnel pretending to be gods would backfire in long-term considerations. Finding out these gods are false will definitely not contribute to good and mutual relations in the long run.
Why pretend?
Be god. Starfleet officers aren't really all that different from gods - they descend from the heavens and propose a pact with unearthly good conditions, then live true to their word. That's what most scriptures tell of most gods, and there's no built-in need for such a relationship to go sour over time.
Second, establishing a physical encounter with a "god" will most likely not contribute to an independent, self-determining and advanced culture but one that prays for help and assistance rather than to get up on its own feet.
Religions don't need physical encounters in order to maintain cultures that pray for help and assistance. Little would change there in practice.
And we have a good example from our own world. I once talked to an Arabian journalist who told me in the face that he can't stand it anymore to listen to other Arabs saying "Insha'Allah" ("God willing") because they don't rely on their own capabilities to actively get things moving, but instead rely on God and wait for things to happen. I'd call that a progress-killer, it stands in the way of "normal social development".
But that's again the Starfleet chauvinist in you speaking. This is merely normal social development for the Arab culture - if you condemn it, you certainly aren't helping the culture along. You are replacing it with another culture of your liking.
In Paradise Syndrome things didn´t work out too well for Kirk as a god.
They didn't work for Kirok. Kirk might have fared much better, considering that the divine acts required were technological in nature.
And the techniques/technologies he taught the natives were probably also in violation of the NID and/or the PD
So what?
They certainly "worked out well", benefiting the local culture without destroying it.
In general, it seems that Kirk doesn't much care for the "do no help/harm" aspects of the PD. Is this because he knows from experience that he won't get punished for it? Or because he knowe from experience that the natives will be better off for it? Or is it simply that the PD (unless enforced in the rare "full" form) does not actually preclude him from doing help or harm when required?
Is saving a less developed or primitive culture (even without its knowledge) a violation of the directives? Did they violate a directive in repairing the deflector to save the planet and thus change its (natural) fate? Or is that sort of interference condoned in the name of "humanity"?
A somewhat more intriguing question is, why did Kirk bother in the first place? He knew there would be an asteroid strike within a couple of months - but he also knew there would be another, and another, and another, apparently averaging three to twelve per year as we later learn ("skies darkened three times since the harvest"). Yet the planet is pristine, obviously immune to asteroids somehow.
It's a mighty coincidence that Kirk/Kirok arrives exactly when the immunity ceases, but a mystery why he arrives at all. If his mandate and orders include saving planets that aren't even in the need of saving, then it's clear that the PD rather categorically allows for helping when nobody notices, including less extreme cases than this one.
I think it's best to take a look at the Prime Directive and its most basic and essential intention, which is apparently the "protection" of a less-advanced civilization.
But that's not its dramatic function, which leads to it not being its in-universe function in practice, either. Essentially, we are dealing with a rule that ties the hands of our heroes, so why not treat it as one in-universe as well? Surely there would be obvious reasons for limiting the freedom of action of a starship skipper. His most innocent keypresses alter the course of galactic history, his innocent smiles and friendly worlds topple kingdoms. Telling him to keep his hands off a number of things is a good start for a list of General Orders!
Thus I think "protection" and "preservation" of an alien culture are somewhat synonymous
Wouldn't "preservation" rather equate stagnation, which apparently must be eradicated even with the force of arms if necessary?
The Preservers set up an entirely unnatural situation in the first place. And why did they select a planet so likely to get pummeled by rocks from space that a deflector was needed? Or perhaps that was the Preservers' intent—let the colony be wiped out by their own character flaws (Salish's predecessor jealously failing to share the knowledge of the temple). In that case, why did the Preservers "rescue" the tribes at all? Many TREK episodes don't bear close scrutiny.
This is another case of things becoming clearer if we keep on watching the Star Trek universe unfold. "Paradise Syndrome", "The 37s" and "North Star" all seem to describe the popular custom of abducting Earthlings nobody will miss, and the latter two involve putting said Earthlings to forced labor. Why not the first one as well? Primitives cannot mine asteroids - unless asteroids are brought down to the surface of the planet by deflector beams.
Possibly the Preservers set up a labor camp but didn't have time to get the industry going (or had to shut it down in mid-run) before they had to run away from the cops. Only one end of their setup was now in operation: the one chucking asteroids towards the planet...
OTOH, the planet was clearly terraformed, and neither the Briori nor the Skagarrans were credited with terraforming abilities or ambitions. Abducting slave labor is probably dirt cheap, but terraforming must be expensive... So we might be talking about a more venerable culture that used asteroids for raw material, but disappeared, leaving behind the perfect setup for ruthless criminals...
There's also the intriguing fact that the incoming asteroid is a whopper. "The size of Earth's moon" means ginormous as far as asteroids go - not your prime choice for mining. But since the deflector deals with such things with ease, that's probably not a factor. Hmm. Perhaps it's set to "hold" as the mining and refining operation is not online, and just chucks the same rock, or set of rocks, to a holding pattern over and over?
Timo Saloniemi