Let’s look at the even-numbered Star Trek movies. They’re considered good pop culture, and tonally, they’re all over the map, so they’re a good example.
Counting backwards, VI is a blatant allegory for the end of the Cold War. IV has an explicit message that was trendy at the time (“Save the Whales!”), and became the iconic example on TV Tropes of making up an absurd fictional consequence to frighten the audience (“Or else aliens will destroy the Earth in three hundred years!”)—but that’s largely because the movie is a comedy with all the Star Trek characters in the contemporary San Francisco Bay area, and the plot is an excuse to get them there. The message of the movie is not really its theme.
The there’s II. It doesn’t have an explicit message (although Khan, Spock and Kirk all do get speeches about what they think the lesson of their lives is), but it has themes. Big themes. The director and screenwriter, Nicholas Meyer, has talked bout how those developed around the needs of the production: Leonard Nimoy was ready to stop playing Spock, so Meyer saw that the way to lure him back to make the movie was to promise him the chance to play a great death scene. Originally, that would have been closer to the beginning, but in rewrites, it kept getting pushed later until it became the climax at the end. This got Meyer thinking, “We were giving birth to planets, and Kirk was meeting his son, and Spock was dying. You sort of looked at that and said, ‘Well, what unifying ideas are running through here?’ And then you thought, ‘Ah! This is going to be a movie about…’” At that point, Meyer decided, “This was going to be a story in which Spock died, so it was going to be a story about death, and it was only a short hop, skip, and a jump to realize that it was going to be about old age and friendship.”
So all of these are popular, well-reviewed movies that have stood the test of time, and are liked mostly by the same people today, but in terms of themes or messages they’re all over the place. The consensus is that the most serious movie, the one About Growing Old And Friendship And Death, is the “best” Star Trek movie. That isn’t sarcasm: a lot of people have a real emotional reaction to that, especially people who grew up with the show and saw the movie as they got older. But it’s also not as if First Contact needs to be about anything more than saving the Earth from the bad guys and maybe a little about PTSD to be considered a good Star Trek movie.
Or if you’d rather use books as examples, Lord of the Rings does have things for academics to talk about: it has literary motifs, allusions to mythology, the preeminent set of constructed languages in all of literature, and even a few homilies on topics such as capital punishment, but it’s not in any way a book about big ideas. The Narnia series, written at the same time for a similar audience, does have big ideas (with The Silver Chair expanding Plato’s allegory of the Cave into a setting and giving it a Christian apologetic twist), yet today it’s mostly written off as preachy Christian books for kiddies.
If you look at the kind of literature that people usually call “great,” and study in literature classes, it typically tries not to sound didactic. That’s considered a mark against it. The kind of person who talks about what a work really means doesn’t want everything spelled out for them. Also, if a work of literature is trying to argue for a political point and is universally considered great, then almost by definition it has to be saying something that everybody agrees with. Treating anyone but a small child as if you have to spell out the obvious to them is going to come across as condescending (Although a lot of the best books with a political message are for one reason or another disqualified from being assigned to children: they have upsetting endings, all the better to motivate the reader to get up and change the world, or they deal frankly with sexuality.) Even so, some books in the Western Canon do have an explicit moral. To Kill a Mockingbird, The Grapes of Wrath and All Quiet on the Western Front all have stand-ins for the author tell us how we should feel about what happened. This is mostly, though, a thing of the past. If a work shows a villain having a great time and showing all the authority figures up, until the final scene where he’s punished and the audience gets a lecture about how you mustn’t admire him because he’s bad, a modern audience is going to be extremely cynical about the disclaimer at the end.
More often, though, there’s room for us to make up our minds. People still debate whether Milton was “of the Devil’s party without knowing it” when he wrote Paradise Lost, or whether he was consciously being subversive, or perhaps we’re just projecting our own modern viewpoints onto the poem. People disagree about whether Shakespeare meant Brutus as a villain or a tragic hero. But these works touch on big, universal themes that people still care about and identify with today.