I don't mean the books are good – though, they are, and you'd very probably enjoy reading them – I mean they are perhaps the most potent introduction to literature appreciation for readers today.
As your annoying English teacher in school used to say while you weren't paying attention, (some) stories have something called themes. This is a very slight misnomer – they're only thematic because, when fiction wants to make you think about an idea, it presents it many times and in different ways, different views on the same idea. Noticing an author uses the color green a lot in some circumstances is just the first step – the purpose of noticing is to look at the ideas of the work in a particular way, a perspective frequently too weird or unpopular or impolite to say explicitly.
It isn't until some children read the perspective of someone so... intensely off-putting... as Holden Caufield that they start realizing, hey, angst is pretty pathetic and strange and self-victimizing. You could just tell people that, exhort them to more compassion and forgiveness and cooperation and humility and optimism (because, ya know, things are pretty good and not seeing that is odd). But, ya know, that doesn't have the success rate you'd hope for. So you tell stories.
But mostly you need people to actually pay attention to stories. Writing essays about them, as your teachers undoubtedly forced you to do, is not a silly way to get the ball rolling. That core bit of careful reading is where all the magic is, though.
A Song of Ice and Fire is the most closely read piece of modern literature (it's probably best to treat the series as a single work) outside of religious texts [n.b. religious texts being the far-and-away winners on this metric is no coincidence, and pulling lessons from stories is a core task of bible study, to be sure, but there's something to be said about peer-to-peer wisdom transmission, and whatever you think of your local church, you're not seen as a peer to their holy text, which limits the questioning of wisdom you'd get with more critical literature review]. I think – Harry Potter certainly is a strong contender, though out of the spotlight more and more, obviously. But ASOIAF certainly has a lot to say.
Of course, this is because the author cheats! His setting is faux-historical, a context liberally copied to present many of the same insights he came to in his detailed studies of history. He doesn't have to be unusually wise, just present a story in the context of lots of incidentally wisdom-enhancing interactions between people. The difference between a good person and a good leader, the more natural barbarism of man and how fragile peace can be, the virtue and danger of honor and trustworthiness, how to notice when to ignore a salient and emotional conflict to do something bigger – which is what the whole process of peace actually looks like, to say nothing of how he's depicted the truer horrors of war.
Of course, these aren't insights about coming of age or what it means to be a parent, like "great literature" ought to be – although, you'll notice, many characters do come of age, and there are many examples of better and worse parents and how that impacts their family over time. It is genre fiction, as many sneers as that may invite, but it's better classic literature than most examples in the modern western canon.