"Friday's Child" is spared the award - There's nothing generic about this story; I'm amazed it didn't get knocked off the list sooner (I think it's nigh on a classic), but I'll endeavor to explain:
...From recollection as I saw this last autumn...
Friday's Child:
* has no computer running the joint so Kirk has to find something to do other than nagging it
* deals with another culture they've had limited experience with, for which Spock and Kirk - who aren't diplomats by default (think Ambassador Fox and others in previous episodes) - didn't remember all the nuances of during their study so when Ding-Dong-Security-Dude acts really dumb and gets killed while forgetting while they're there on the planet to begin with, they now have to splutter while in a diminished position to this new culture -- but it all helps set up the drama and sense of threat very palpably.
* it's a no-no to touch the leader's wife
* she doesn't want the child when the leader is murdered because the child would be seen fairly badly, never mind being competition for the throne (and for the (1960s, this is big stuff to go onto network TV)
* internal power struggle within the culture that Trek didn't use terribly often (the only other time I recall is "Balance of Terror" but not given the extra layer)
* McCoy bravely risks all to help her save the child she does not want
* Julie Newmar and Ben Gage really sell it with their performances, so does Kelley given what McCoy has to deal with
* the dramatic entanglement with the Klingons works rather well, despite being shoehorned into the script!
* we don't often get distress calls, legitimately or as decoy - which is very nicely handled
* who could hate the location filming at the most overused oversized rock pile on this planet, Vasquez Rocks(tm), since everyone goes there and almost never do people recognize the area due to its layout. Maybe once in Buck Rogers but that was a gaffe...
* reminds me of the bop pop song "Saturday's Child" from The Monkees, solely because of episode title name.
* "Friday's Child", from an old song, means "
loving and giving", a subtle nod to what the child would likely bestow on the people. (A song that happens to be
a cappella, noting the planet and civilization on it...

)
* Spock gets a hilarious line at the end of the episode once the baby's name is revealed
I just looked up the episode, why not:
* this is the first time Chekov falsely attributes something as a Russian invention. The trope gets very generic very quickly in later episodes, however...
* Roddenberry objected to the script having Eleen killing her baby. The story's reverence on life in general is part of Trek's more underlying themes so I can imagine why Roddenberry objected to the original script.
* DC did write Eleen as a strong female figure to fight against her society that was very narrow of its treatment of women (only as mothers/homemakers), which helped culminate in the original ending of her baby being sacrificed (which is remarkably strong and seems almost harsh (?) but I do wonder what else of the episode was changed at Roddenberry's behest. I'd be a treat to ever see the original draft before it all got changed. Would the story be more or less poignant? IMHO the finished product works but the original vision of the creator, Fontana, definitely wanted something a bit different. And, of course, the network may not have wanted the original ending for reasons similar or otherwise to Roddenberry's... again, for 1967, it was pretty big.
* Eleen is still strong but I suspect she was a lot different in the first draft.)
* the real reasons for "Capella" are stated

* Oh, Chekov ditched the Monkee wig by "The Apple". Thought he still had it on, oops...