1. Something appears a little off in the definition of the greatness of a novel: "they reveal the inner thoughts and feelings of the characters." There's a certain sort of novel for which that's true--indeed, some of my favorite novels: 19th century, particularly French and Russian. To put it differently: I think it explains why Crime and Punishment is a great novel, but not why David Copperfield is a great novel. Dickens makes the Murdstones more sinister by giving us less information about them--opacity is a great virtue in literature. Then there are unreliable narrators who one can't entirely trust in reporting their own thoughts and feelings (an interesting example of this is Portrait of the Artist as a Young Man in its earlier sections)
2. Quite apart from this, the comparison to songwriting is apples-and-oranges.
The typical song is about angst, lust, longing, etc. You know, teenage emotions. So, of course, a teenager or 20-something can write a song about them. The depth, scope, and nuance required to write a novel necessitates somebody who has had more life experience.
I will attempt to explain why by bringing in a third area: poetry. Some poets only work when they're young (Rimbaud) or notably flame out (Coleridge), but I'd have a hard time pegging the latter's writing in "The Rime of the Ancient Mariner" to a 25-year old sensibility, though my math indicates that's approximately when he wrote it. Subject and method and technique vary wildly over a career.
3. Two interrelated phenomena are also difficult to explain in this framework: the first-novel-only and the end-of-career-malaise. In music, as in the novel, there are no shortage of people who are able to write one good book/album, and never replicate the feat. But if a sensibility improves as it ages, why wouldn't the depth or insight of a follow-up work increase? As to the second, see the late-career declines of Eliot and Auden (one can presumably think of writers who crank out monotonously similar novels at the end of their career, like Maugham's mock-Hardy does in Cakes and Ale); their declines extend, I think, even beyond their creative to their critical work. Why the muse comes and then leaves--that no one really knows.