Saying "Conspiracy" was the best episode of the first season is not saying a whole hell of a lot.
But it was nonetheless; it has a mixture of paranoia (with the dark whispers of an evil conspiracy soon followed up with brutal destruction) and revulsion (aliens eating bugs, icky). If Tasha Yar initially started out as an idea to put Vasquez from
Aliens into Trek, well, this was going after the title characters themselves. This is part of why it feels so un-Trek, also - the tradition of turning the Other into an inhuman, monstrous force that must be destroyed at all costs is common enough in sci-fi; a staple premise of the
Alien franchise... and mostly alien (ha, ha, I am a joker) to
Star Trek, which invariably tends to humanise the Other. It doesn't matter what monstrosity is out there past the stars; I'm sure even Cthulhu will see reason after a few diplomatic conferences. That's the
Trek way.
The out of character aspect of this episode doubtless also has some of its appeal - there's not a lot of
Trek, and even less of TNG, where Picard reaches the conclusion that the one solution is to just shoot the bastard.
And also, that it was Picard of all the Captains who did it (Riker too, but this is sort of his thing...).
And the alien leader pretty much presented them with Fed values (We just want to get along) which makes Picard blowing him up the more surprising.
Not really. Their actions indicated they weren't looking for "peaceful coexistence." Taking over Starfleet HQ, attacking and killing people took any legitimacy out of that claim.
Even if we ignore their actions, consider what peaceful coexistence means for them: Parasitically controlling our bodies. That's what Remmick means, and that's not the sort of thing the Federation tolerates.
Well, unless you're a willing host like the Trills are.
IIRC, they were worried that the episode might be a bit too dark until Gene Roddenberry okayed the thing.
The original idea for the plot - hinted at in "Coming of Age" - was a real Federation conspiracy. But Gene vetoed the idea of Starfleet officers conspiring, so alien bugs were used instead.
In turn, these guys were going to be used in a follow-up story but the cost proved prohibitive so we were given the Borg instead.