Kirk had amnesia in "The Paradise Syndrome". All the futility was by ever-logical Spock.
The mission always was to deflect the asteroid, even before our heroes beamed down and Kirk got lost in the basement. And even at this point, all the heroes already knew about the "asteroid alley" thing and the futility of deflecting merely one of those. Kirk really was willing to wrestle with giants for the slightest excuse...
There might be 2 reasons why Boraalans weren't placed in stasis.
1) Maybe there wasn't information about the Boraalan body, placing them in a standard stasis "field" might have killed them, so without more studying, there was no way to take the risk.
2) It would've made a boring episode.
0) It wasn't Picard's decision or desire to do anything about the Boraalans in the first place. Only Nicolai was doing anything, and he didn't have the resources or clearance to try anything as complex as stasis (which in VOY requires either the careful setting up of sarcophagi for all the patients, or advanced longterm trickery with the transporter).
Picard says at the end something along the lines of "Did we cause as much damage as the stellar fragment"?
Well, that's a pretty valid question. The answer might be very close to "yes" - these people had continued eating, breathing and breeding because they believed in certain narrow-minded ideals. Thanks to the help from Picard's crew, their entire society might well be dead in one generation.
What would Kirk have done? The problem of the week was solved by applying 24th century technology through a very large and powerful starship. Kirk would have had access to neither. So Kirk would probably have organized an evacuation somehow. Could he have devised a means to keep these people happy and free to follow their own path? That's not our Kirk - he forces people to abandon their dreams and dance to the Federation tune. So there wouldn't even have been a problem that particular week, just a standard evacuation mission.
Ship's captains should be trained to know when the prime directive applies and when it doesn't, and have the personal wisdom to know the difference.
But that, supposedly, is the very purpose of the Prime Directive - to stop starship captains from ruling the universe however they see fit. The rule doesn't protect native societies from Harry Mudds: civilians are exempted. It just ties the hands of starship captains, and justly so, or else there would be no point in having a Federation government. Conversely, the government is the one with the mandate to think, so it and only it can waive the PD.
Beyond this, it's just a matter of proper delegation. The Federation Council can't be on the spot every time to solve all crises hands-on like some North Korean great leader. So the skippers have to be given some powers of decision. But the limits can't be soft, and the erring must always be on the side of caution, or else too many societies will be destroyed per week - sometimes many times over, as every visiting starship skipper has his own ideas about what is a proper way of life and what is not.
Timo Saloniemi