Well I go under the assumption that the Federation is an organization that is moral and just, and not greedy and corrupt like real life empires like the British Empire. In the case of the British Empire subjugating India, it was done to steal resources under the premise that they were "enlightening" the local population.
No. Maybe to some extent, that was a factor, but to a large extent, a lot of British subjects sincerely believed that they were there to improve the way of life of the people they colonized. They assumed their cultural values were more "advanced" and more "correct," and that the natives would inevitably be happier once they assimilated.
The only reason Gandhi's campaign of passive resistance worked was because the rank and file of British subjects believed they were doing the right thing, that they were the good guys. By resisting without violence, by employing civil disobedience and accepting the consequences when they broke the law in protest, Gandhi and his followers proved that they were not unruly savages needing to be civilized, but that they were already reasonable, moral beings. And thus, when they were oppressed by the British Raj -- or subjected to brutality like the massacre at Jallianwalla Bagh -- the British people were forced to recognize that they had become the bad guys, that their good intentions had gone horribly astray, and that it had to stop.
See, this is the danger of
assuming that you are just and moral and wise. As long as you accept that without question, you can rationalize anything you do, and dismiss any opposition as misguided. The Prime Directive isn't really about the other culture -- it's about your own culture. It's about having the humility and self-awareness to recognize that you don't have all the answers, and that even a well-intentioned effort to make another civilization's lives better according to your definitions of "better" can go horribly wrong.
I make the assumption that the Federation is not such an organization, and that Federation assistance of a primitive race might genuinely be helpful to them.
But considering them "primitive" at all is itself judgmental, condescending, and dangerous. It carries the built-in assumption that you're better and smarter than they are and thus more qualified to make decisions.
In the case of Who Watches the Watchers, the Mintakans were already at a pretty socially advanced level. Their technology might only have been at the level of prehistoric tribes, but their social way of life was actually more like the renaissance period of Earth. They themselves requested assistance (they said "but there's so much you could teach us!") but Picard shot them down saying that this too, would be interference. Sure it would be, but would it have been wrong? Those people were clearly ready to handle the knowledge. I could see them in a few decades starting to slowly integrate into the Federation.
But we can't assume that's the right or the only path for them. Just because something is your way, that doesn't make it the best way.
And no, they didn't "request assistance." That's more of that condescending, White Man's Burden thinking, the reflexive interpretation of other cultures as needy and dependent on your superior benevolence. What they did was to
seek knowledge. They wanted to learn more about the universe. But sometimes the worst thing you can do for someone seeking to learn is to just hand them the answers. Then they won't develop, or retain, the skills to learn those answers for themselves. And who's to say they won't find new answers that never occurred to us? Again, just because something is our way doesn't make it the only possible right way.
Reminds me of the movie "When the Earth Stood Still" where a sort of "Federation" sends a representative giving humanity an ultimatum regarding its nuclear technology. That is considered a classic masterpiece pretty much unanimously. If it had been Star Trek's Federation, no one would have ever been sent at all.
Nor should they have been. The society Klaatu belonged to was horribly dystopian if you think about it. Everyone lives in mortal terror of the robot masters who will annihilate them if they lift a finger in violence? That's not a peaceful, enlightened society, that's galactic slavery.
And really, Klaatu is very much an embodiment of colonial-era assumptions and attitudes, the wise, stern, paternalistic figure who comes into a more backward society and gives them the soft-sell for converting to his ways while letting them know that they'll be forced to conform if they don't voluntarily embrace the "right" way of doing things. In light of modern, post-colonial thinking, it's a rather problematical film conceptually, though it's still one of the greats.
I think the PD needs to have more leeway in letting Star Fleet captains make decisions based on common sense. I think it's implied that usually when a captain breaks the PD, if he can make a good case as to why, most of the time the Federation forgives the act.
Now, that I'll agree with. An absolute "never interfere" rule isn't wisdom, it's just using rigid legalism as a substitute for judgment. The point of the PD is to teach us humility, to help us recognize our own limitations and fallibility so that we don't blindly impose on another society in the name of what we assume is right. But as long as we have that self-awareness, we can nonetheless recognize circumstances where it can be valuable to offer our help, within limits.