Even the most superficial of Star Trek movies (Nemesis) has some philosophy to it. In the case of the above movie it's about Nature Vs. Nurture. TWOK and FC both have shades of Moby Dick and the nature of revenge albeit told from different perspectives. They manage to put those elements in the movie while telling an entertaining story for the most part. The same IMHO can not be said of Star Trek XI it's all about explosions and lens flares.
Almost every Trek film was approached, to a greater or lesser degree, as if it was going to be the capstone in the Trek franchise. As such, they tried to make sure that it hit every button (humor, pathos, action, philosophy). So there may be an A plot or theme but there is also a B theme or even a C theme.
This is certainly true of Khan. At a superficial level, the movie is an excuse to construct an over-the-top villain in which to hang action set-pieces. But at a deeper level, you have the character arc of Kirk getting older and facing mortality. It is basically a TMP do-over where Kirk starts out an Admiral and reassumes command, but this time with all the character interactions done right.
As someone entering into mid-life myself, I find the themes Kirk wrestles with in Khan to be increasingly relevant and thought-provoking. Kirk's line "How we deal with death is at least as important as how we deal with life" is the deeper theme of the movie, which then plays out to its conclusion with Spock's sacrifice. "The needs of the many..." line is nice, but I find Spock's line "I never took...the Kobayashi Maru test. What do you think of my solution?" to be the more poignant. It is contrived, yes, but so satisfying.
Khan is an excellent example of classic Hollywood filmmaking where everything is there for a reason and the questions that it raises all get answered by the end of it.
It is really an excellently written movie.
The problem with popcorn flicks is that they are basically porn. They dazzle the senses, which is fine, but there's nothing else there. JJ Trek pays lipservice to Trek's themes. Even the flashback scenes of Spock being badgered as a kid. They just don't seem sincere or at all integral to the plot. JJ is all about spectacle, not character, and he paints-by-numbers out of the superhero playbook, right down to establishing Kirk's moses-like special origin. It makes for big box-office but it is not what Trek was ever supposed to be.