I can agree with you on the mcoy spock thing, thats a good example and at the least is one worth arguing about as a debate point, but yeah, the ds9 example was a bad one for reasons already mentioned. The most encompassing one being the argument is that starfleet in general helps each other out, or at least doesnt actively sabotage each other, and the factors you brought up werent federation. There were federation crew conflicts, oh my yes, plenty in all the various series from tos to ds9. But even then, it was REALLY rare to see someone stab a coworker in the back out of malice.
My favorite bit of trivia is knowing that root beer scene was improv. They were literally just making it up as they went along as some b roll filler but it turned out so good that it was put in the show. I LOVED that scene.