"The Inner Light" is one of those episodes that can really reach into people's emotions and touch them. Of course, how far it can reach in depends on the viewer's mood. And how some people are totally unphased, it reminds me of the 2nd season finale of Babylon 5, how Koch emerged from his encounter suit, and each saw a different angelic image (Vorlons seeding their culture with an illusion tailored to their race to make them innately associate Vorlons with good) but the Centauri Londo saw nothing at all. The Babylon 5 equivalent to "The Inner Light" is "Sleeping in Light" though.
I don't know about "City on the Edge of Forever". It has more emotional pull than the average TOS episode but I think at least half a dozen or more episodes from various sci-fi or dramatic shows from the 80s- early 00s have outdone it in emotional effect (if they revisited it, a drugged up McCoy could find another Guardian gate inside an asteroid and we could have "For the World is Hollow, and in the City of Forever I Have Touched the Sky Inside Spock's Brain").
And I've wondered about a few "what if?" versions of "The Inner Light". How poignant would they feel if they had different musical instruments besides the flute? What if the instrument was an accordion? What if it was a saxophone? What if it was a harmonica?
Imagine, the probe is opened and Picard gets sentimental over the accordion and plays it in an emotional fade out shot.
I think "The Omega Glory" is very underappreciated--there are some great sci fi concepts in there. A lot of people apparently have a knee-jerk reaction to the parading of the American flag and the concept that the ideals expressed in the preamble to to Constitution are something we should aspire to.
THAT'S not why people have such a knee-jerk reaction to it. If "The Omega Glory" was some Days of Future Past-like alternate future for Earth, it might have been very well received, but what makes people show utter disgust with what many consider a great episode up to that moment (for the captain violating the Prime Directive for self-gain and the character has a pretty strong presence/is memorable) is this is an
alien planet, not Earth and the Yankees vs. Communists is very thinly veiled. People don't like allusions to be so blunt & transparent. Same reason why Twilight Zone "The Mirror" is seen as reactionary propaganda. The character (played by Columbo) is a thinly veiled Fidel Castro. It crosses the line from a good story into blatant propaganda. The episode up to that point was captain vs. captain, the highly-held principles of the Federation & Starfleet vs. selfishness & exploitation, a conquistador in a New World, but that last act makes it veer into an appeal directly to the audience in some kind of reflective desire to affirm one's patriotism and hatred of Soviet Communists. It's not like everyone who hates "The Omega Glory" has a soft spot for the Soviet Union, it's that they find that revelation very patronising and disconnected from the rest of the episode. That planet ain't Earth* and there's no hint of the Preservers.
*: TOS muddied things up with regular space/alien worlds and parallel Earths out there, which kind of invokes Sliders. The idea is stupid from a TNG era perspective. Parallel Earths belong in parallel dimensions, not out there in space. This episode gets tied up in that. At least "A Piece of the Action" can be attributed to archaeologists/historians that taint the culture they're observing.
Same with "The Way to Eden", which is how the old people viewed these new-fangled "Hippies" back in 68/69. Is the acid reference too subtle? I will give that episode some credit though, as much as it maligns those Edenite hippies, it does seem to display some genuine concern, that they are being misguided by pied pipers, leading them to their doom.
