To be clear, I'm not looking to debate whether this is the best Trek film. Rather, I'm asking why so many people see it as such.
I enjoy TWoK well enough, and certainly it is a good film overall. But consider: it is much more militaristic than any Trek before and more than most Trek since, and relatively violent compared to TOS; there is no exploration of strange new worlds; tonally, it is quite different from most Trek stories. (To be clear, I'm not suggesting that these qualities are required for a "good" Trek film -- I'm just noting a few obvious ways that TWoK is unusual.)
In terms of TOS episodes, TWoK is probably most like a combination of "The City On The Edge Of Forever" and "Balance of Terror" -- which, to be fair, are beloved classic episodes, in part because they are somewhat exceptional compared to the rest of the series. So perhaps that gives us some clue as to why the film is so beloved.
In general, TWoK is ultimately about mortality. For all that the film professes to be about Khan, he really is just an Act of God (in the natural disaster sense), creating an unstoppable force that Kirk must humble himself against. The film is really about Kirk learning to confront death -- heightened by the contrast of the new life of Genesis and in his newly-rediscovered son. And that is something that the film did which was new: able to plumb the depths of Kirk's emotional journey at greater length thanks to the larger screen and the longer format.
But, again... it's a great film, but I don't know that it's obvious to me that Kirk learning to deal with the no-win scenario particularly epitomizes what "Star Trek" is (whatever the hell Star Trek actually "is"). In that respect, The Voyage Home seems like the most obvious candidate -- whatever Star Trek "is", to me TVH "feels" more like it than does The Wrath of Khan.
So, why has TWoK earned such a place of acclaim?
(PS: I could write a similar post about First Contact, whose popularity also confuses me.)
Oh, where do I start?
It’s a really, really tight script, for one, with little or no filler. Unlike TMP, it moves swiftly from scene to scene, from setup to setup, establishing its themes of mortality, aging, the inability to let go of the past, the tragedy and joy of moving forward, of rebirth right off the bat, in so subtle ways that most don’t catch it until later or a rewatch.
For fanservice, it makes good use of a loose end from TOS continuity which is simple enough for non-fans to get without much exposition, and memorable enough that old viewers will remember it. The relationship between the Big Three is no longer as broken as it was throughout most of TMP, and the banter naturalistic and enjoyable, even among the supporting crew.
Nick Meyer adds all these little touches in the background that make it ripe for literary analysis. A Tale of Two Cities and its themes of sacrifice, Kirk’s fondness for antiques, never really established before, echoing his nostalgia for times past. In Khan’s cargo carrier, you see on the shelf as Chekov discovers the SS Botany Bay tag: Dante’s Inferno, stacked on top of Milton’s Paradise Lost/Paradise Regained, stacked on top of Moby Dick, showing the progression of Khan’s experiences on Ceti Alpha V, echoing his hope in reference to Milton at the end of “Space Seed” - to rule in Hell, build his own Paradise - now replaced by obsessive revenge.
ST II also sets up TNG, in its way, by introducing Peter Preston, David Marcus and Saavik - essentially Scotty, Kirk and Spock’s offspring - the next generation of voyagers that the old guard are trying to give way to, but the past just won’t let them and indeed threatens that legacy.
And then of course there’s the space battles - never really as well executed due to SFX limitations in TOS - but yet leaning so completely into the nautical and submarine metaphor established by Roddenberry and “Balance of Terror”. It was a risky move in an era dominated by adrenaline-fueled Star Wars dogfight-like starship combat, but Meyers’ direction made it work. There’s never a time you don’t know exactly what’s going on in that battle, or what tactics the two sides are employing.
You’re right in the sense that it’s not traditionally what one expects of Star Trek, leaning more into the pulp adventure mold rather than the aliens and exploration mold. But to a degree it’s still an optimistic future. Kirk’s son and Spock’s daughter ready to take the reins, the Genesis Planet representing the potential for new life, Kirk himself experiencing a rebirth of sorts as he finds his youth restored as his best friends told him it would be - on the bridge of a starship. But who says the final frontier can’t be inside us, too? (Archer said as much)
And in the end, it’s a complete movie. The forced-on-Meyer shot of Spock’s torpedo casing notwithstanding, it’s a complete story from start to finish, with no “The Human Adventure Is Just Beginning” tease or the sequelitist tones of the next two movies. All the information you need to know is in here. You could watch it without tying it to a larger universe and be completely satisfied with the experience. All you really need to know beforehand is that it’s connected to this TV show from the 60s.