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.)
The problem with crowning The Voyage Home as the best Star trek movie is that the Enterprise is absent.
It's not like you need the Enterprise for good Star Trek. Many of the best episodes have not really used the ship. But for a movie to be the pinnacle of Star Trek in fan reactions, the absence of the Enterprise is keenly felt.
If I was going to put any movie up against The Wrath of Khan it would be the Undiscovered Country. Everything I like about TWoK returns in The Undiscovered Country. An iconic and interesting antagonist? Check. A starship battle decided by clever outthinking of the enemy instead of a situation where the main character and antagonist end up in punching match? Also check. Kirk confronting his place in a world that keeps passing him by? Also check.
If I had to ask why does TWoK beat out TUC, and it only does by the narrowest of margins, it's that TWoK has slightly more universal themes. The Undiscovered Country is about the end of the Cold War, and if you grew up in that time, it resonates strongly. Treating your old enemy with respect, moving past your old hate, these are things which landed much harder in the early 1990s than the early 2020s.
But growing old, life passing you by, old mistakes coming back to haunt you, the danger of revenge, all those stand out today as well as they did when the movie first aired.
TWoK aged better than the others, though not by much. Many of the other movies are very, very good. I personally rank TUC and TWoK almost even.
I do think TWoK has in my mind soured a little for the same reason that First Contact did. Its success ensured we'd get so many attempts to dip into the same well again. But that's a very subjective issue, and one which it's hard to really hold against TWoK.