I didn't say anything about Roddenberry.
The no-conflict dictum had come from Roddenberry. Maybe someone can cite what it was he said exactly, because I don't have a reference handy at the moment. It was something to the effect of "our crew gets along" in order to nix emotion-driven interpersonal drama as too petty.
But more importantly, none of them involve conflict among the flagship crew.
"The Pegasus" does, in fact. Rather famously. It's the one where Picard threatens to revoke Riker's status as XO.
Oh right, my bad. You're right. This was a nice exception. However, note that this involves Riker's loyalty being divided, by having been influenced by a past officer who does not serve on the flagship. That other captain is the bad guy who corrupted Riker. Loyalty is a virtue in Riker that the other captain had taken advantage of to serve his own personal ambition and evil ends.
The "no conflict among the crew" dictum also went rather by the wayside over the years -- not just Pulaski (and agreed there), but also Ensign Ro, Reg Barclay, Picard vs. Wesley at the Academy, Worf vs. Data during a stint by Data in command, and so on -- with variable results. There was never a stable "X is assigned to constantly bicker with Y" dynamic, obviously (and frankly that's to the good), and major conflict among the core cast stayed rare... but their being "perfect" insofar as it was ever a thing really wasn't a thing by third season.
The only one there between two regulars is Worf/Data, and neither is even human. That example can't contradict the idea that humanity is superior/has a superiority complex in the future, if it's a dynamic between an artificial person and a member of an aggressive warrior race.
Ro isn't human either, come to think of it. The issues she's struggling with, human though they may be, are shoved off onto an alien race who had been beaten down by another aggressor. She has to bring the flagship crew emotionally to see her side of the Bajoran situation, and ultimately she is unable to bring them all the way to her position. TNG-era
Trek's effort to show a crew with divided loyalty on the Maquis issue (VOY) was basically a miserable failure, because overall that conflict was wrapped up pretty quickly.
"The First Duty" was an episode where it was a welcome thing to see Wesley getting in trouble, but again he was no longer a regular by then and he had fallen under a bad influence. Again that's rather like the Riker example with the bad influence trope. The bad influence isn't aboard the
Enterprise.
Which is fine, you don't want bad influences aboard the ship. But there aren't even any character defects in the regular cast either (
edit - I mean of the kind driving interpersonal conflict within the regular cast). Reg, the neurotic, isn't a regular, and in fact he's a good example for what I'm talking about. The conflict with him was that he didn't fit in. Pretty much everyone had a supercilious attitude with respect to him, and they wanted to get rid of him at first. But he wasn't a regular. He was a singular oddball.
Now, to really contradict what I'm saying, what they should have done was taken Reg's holo-addiction and given it to Geordi, post "Booby Trap." Don't have him fixate on Leah, but have him descend into a fantasy world making crew parodies. Then you would have had a regular with real emotional problems, with something for Troi to really do as space shrink.
We're kinda getting off the TOS track though, discussing TNG.