Are we sure that classical art aims to deal in truths and psychological insights that are more universal? I'm not sure that is always the case or even most of the case.
Of course it doesn't, depending on what you mean by "aim." A great deal of what art represents and signifies isn't a result of conscious "aim." The more abstract arts such as music may not aim at anything but delightful and satisfying form, but that is far from from a meaningless objective. The perception and love of form is fundamental to our very natures as conscious beings, and so the play of form, both as the abstract expression of mental activity and as the representation of human gesture, utterance, and the trajectories of emotion, is a primary focus in the music we call "classical." Popular music tends to go no further into the exploration of form than it needs to in order to get its explicit message across.
I also can think of many popular songs that deal explicitly in issues that classical music only rarely touches if at all. They don't last as long as some classical music (of which Sturgeon tells us accurately 90% of which is crap) due to the fact that another song comes along to displace it,
Popular art is almost always explicitly
about something, namely the concerns, events, fashions and sensibilities of its time. That's one reason why it tends to be - though it needn't be - more time-bound, more ephemeral. Classical music often ensures its longevity partly by not being explicitly "about" anything, though it may definitely be about something not, or only roughly, describable.
What is more profound that the realization that humankind is driving the world's wildlife into extinction through environmental vandalism? Listen to Ian & Sylvia's Antelope. Listen to PJ Harvey's album Let England Shake. There are innumerable songs about good love, bad love, and everything in between, with the music well tuned to the lyrics. Even songs about life and death (of all things)! The Blues. Cante flamenco.
Again, explicit "aboutness" does nothing in the long run to ensure music's attractiveness beyond its time and place. It may have the opposite effect by limiting the precious flow of ideas from the artist's subconscious and so narrowing the "aim" of the work and its possible meaning for listeners, present and future.
The longevity of CM is largely the staying power of its audience, attuned as they are to hearing the favored old familiar melodies over and over. That and the intellectual/social panache of being counted among the Best and Brightest People. That includes me, though I certainly also love the music--among many musics--very much. I await somebody telling me that I cannot possibly love CM as much as they do or as it is correct to do so.
What a load of #@$%&*$#.