There’s another half to the Prime Directive that doesn’t get mentioned often. I didn’t see anyone mention it above, and I apologize if someone did.
When people discuss the Prime Directive, they almost always discuss it in terms of protecting the native culture from contamination. But the part that doesn’t get mentioned often is that the Directive also protects Starfleet from the moral burdens of caring for less-developed cultures. Let’s say that Starfleet made some sort of Herculean effort to protect the planet or relocate the people. That then sets a precedent by which they should also save the next planet that is in peril. If we want to take that logic to its obvious conclusion and say that Starfleet bears moral responsibility for their inaction, it follows that they should be intervening in every culture so as to share their medicine and technology. After all, they want to save planets in danger of destruction, but aren’t people also dying of disease and famine and internal wars?
In short: The Prime Directive insulates Starfleet from responsibility for shepherding every single primitive planet they encounter.
I don’t mean to threadshit here, but I’d like to give some real examples of how this plays out. Back in the 90’s, the USA chose not to intervene in Rwanda. The logic was that we had no reason to intervene in someone else’s civil war, when we had no strategic interests. The fact that it turned into sheer anarchy and slaughter directly impacted many leaders’ decisions to intervene in future conflicts such as Kosovo or Libya.
When I was in Afghanistan, I often suggested to my fellow soldiers that we might need our own version of the Prime Directive. We experienced a lot of ‘mission creep’ in that many of our military goals were being obstructed by Afghanistan’s social problems, which we had neither the expertise nor the mandate to resolve. I won’t recall the details here, but there were also well-publicized incidents in which soldiers had to choose whether or not to intervene in Afghan civilian crimes, despite the fact that they had no mandate to participate in Afghan law enforcement.
Anyway, I thought it was a good episode when it first aired. I re-watched it two or three years ago, and I still thought it was quite good. As you’ve gathered, I’m not an adherent of the idea that Picard must intervene, but I agree with OP that once they were brought aboard the ship it becomes impossible to reconcile the problem because Picard cannot morally take the step of executing them. As others have pointed out, this is not so much a matter of Picard being a dick as it is a matter of cultivating the drama in the situation. I agree very much with Tim R. Mortiss that forcing the characters to choose among unpleasant options with competing moral priorities is how you wring drama from the story. If the moral conundrum had a clear-cut solution, it would be a short and boring episode.
I also think this was a good example of the maturity in the scripts we saw in the later seasons. I’ll be the first to admit that Season 7 still had some clunkers (remember, the very next episode was ‘Sub Rosa’) but on the whole they were vastly superior to the early seasons. I really enjoyed episodes in which the characters made bad choices, or had to live with the consequences when there was no obvious ‘good’ choice. My other favorites are ‘TNG: Lower Decks,’ ‘DS9: In the Pale Moonlight,’ and ‘ENT: Damage’