Not just in YA, but also in adult fantasy, the hero of a fantasy novel is prone to be on the young side. Just barely an adult, or on the brink of being one.
It's not exactly new. Some fairy tales have children, young enough to return to the parental home after adventure is done; some, fewer, have an adult who already left the parental home (and possibly even married) going on adventures. But the general plotline is the hero leaves his parents' house (voluntarily or involuntarily), has adventures, marries and settles down in a new home. Legends and myths have some more already adult characters, but then there are reasons for that, and they apply to some fantasy stories as well.
On the whole, young heroes have several advantages for fantasy writers.
If you want to send the hero on a quest, who is he leaving in a lurch? Spouse, children, job? A little less than heroic there. No one? But if it's no one, how did an older character manage to get to his current age without acquiring responsibilities? A little self-centered, there, mostly likely. A sixteen year old, or a twenty year old, on the other hand, can have no responsibilities without any more reason than age. And in the reverse manner, compared to a child, we have fewer questions about how his parents (foster parents, guardians, what have you) let him go.
This reasonable lack of responsibility is part and parcel of how the young character has more room for growth. The character can grow, mature, develop -- and not raise so many questions about how he started out so immature at his age. Developing abilities and learning about the past are less time bound, but if the character is older, it may raise unsettling questions about his lack of curiosity.
Plus romance subplots. The absence of a spouse and children is crucial here. And the question of why the hero is still unaffiliated at his age is even more pointed. Is there something seriously wrong with this person, such that no one would want a romance with him? At least in your classic high fantasy. Modern-day fantasy is more flexible, as are fantasies set in similar cultures, because modern culture is more flexible. Not marrying young may still need some explanation, but nothing so much as if the character was a noble in a culture with arranged marriages. (By the same token, it boxes you in on your world-building.)
Also, it is reasonable for the young hero to be a green adventurer. You have to explain why an older one is ignorant before you can use informing him as a way to info-dump.
On the symbolic side, characters at these ages are liminal. Neither adult nor children. Goes hand in hand with all the other liminal traits they often acquire -- going on journeys, to be in neither one place nor another; transforming into a wizard, or a swordsman, or a king -- and reinforces them.
This, of course, does not apply to all genres. Ancient myths and legends frequently had fully adult heroes, and so does sword and sorcery, drawing on it. On the other hand, only certain types of characters would voluntarily take on these roles. A character might, like Bilbo Baggins, oscillate between home-body and adventurer, but anyone who seriously loves settled life, or even peace and quiet, will choose a job with less travel and dangers. Anyone who thinks of adventure as someone else having a hard time a long way away is out. (Involuntary brings its own problems, too.) Their motives tend to be a love of danger or a need for money. They start out on adventure when younger and thus are experienced and knowledgeable, and making them not much use in informing readers. Romantically, they are notoriously love-'em-and-leave-'em types. This, of course, limits the possible characters.
Then, even in genres where all the young hero's advantages apply in full, they can be finessed. Massacring the hero's village is such a good way of disencumbering him of all responsibilities (and leaving him open to new romance) that it's a cliche, and even used on the younger heroes -- partly, of course, because of its other advantage, namely powerfully motivating the hero. Threatening or kidnapping the family can also be used in the same manner. Conversely, making him unable to marry or either take or keep a job he finds meaningful can give him a motive to escape the situation, particularly if the reason is not bad luck, but that people were treating him badly. Or even a character who has reasonably lost responsibility, such as launching his youngest sibling into an apprenticeship.
Still, even if you start with the notion of an older character, you have to somehow make the finessing work in the story. It's not enough to throw it in. It has to be integral, and advance the story. If not, a younger character may be better.
And it makes me think--Bilbo and Frodo are enyouthened by wealth and (unexplained) lack of personal attachments. And of course, as hobbits in their 50s, they are more like humans in their 30s ... but rich! Bertie Wooster types, if you will, avoiding strings to hold them down …