I think very young protagonists just don't work for the type of stories that games want to tell. The 17-24 range is really problematic for the foisted on leadership roles that some RPGs try so very hard to foster on you - particularly Bioware games. The best Bioware take on this actually is in ME1-ME3, where Shepard is (1) older, starting the game at 27 (as I recall); and (2) doesn't have much of a say in the broader mission parameters, those decisions being left to more senior persons in more senior command positions. Whatever independence Shepard does have comes from the plot contrivance - being a Spectre, then being with Cerberus, then having pre-existing relationships with so many important figures and the undetectable Normandy, winning the job of stealth diplomat by default.
Older, established individuals do not just give up authority to someone who is young just because it happens that this young persons is really awesome at killing or is otherwise unreasonably well-spoken. This time of power fantasy, IMO, is actually more unrealistic than the usual complaints people have re: the unrealistic nature of romances and fawning over the protagonist in general.
I think it depends on the context of the story.
For a story like DAI, you are given power over others because you have a special ability that no one else possess. Your age really is irrelevant next to the fact that you are the only one who can close the veil tears. Which I think is a good thing because it allows the player a choice in their protagonist's age, rather than forcing a pre-determined age. Maybe the story seems more believable if you have a 40-year-old veteran in charge of the Inquisition, but I don't think having a 20-year-old youth in charge is all that immersion-breaking either.
I also like the opportunity for character development with a younger protagonist - with an older character, I would think that a lot of that development happened in the past (e.g. "This character's got 40 years under his belt, so what he's been doing all that time? What was his job? Was he married? Did he have children? Which countries has he visited and which people has he met already?") in contrast, with a younger character that development would happen over the course of the game (e.g. "This character's fresh into adulthood, so how's he going to spend it? What will his job be? Will he get married? Will he have children? Which countries will he visit and which people will he meet?")
I know I am planning (game permitting) to play a 21-year-old character who is going to have to mature and adapt awfully quickly once she's put in charge of the Inquisition. So I'm quite liking the idea of starting with a brash, wild youth and seeing her go from there.