First, lets take a reality check about children, what can they do, and what can't they?
For example in some sports they go for younger girls, they are lighter, they are more flexible, flexibility which is lost with age. The sports are figure scating and gymnastics. Also, in China young kids are part of circus schools where they do pretty incredible things.
So dexterity seems to be higher for kids than grown ups. At least some parts of it.
If you've tried to keep up with kids playing, you've probably noticed that they have a much higher activity level than you do. But, they sleep more, they get easily bored and they tire over time much more quickly than grown ups. At least that's my experience; you can outplay a kid, but a grown up hardly ever makes the effort because it is mindnumbing.
Then there are a lot of kids being put to work. They work long hard days, for example knitting carpets, sowing footballs or your sneakers.
For intelligence and wisdom. There are kids as young as 9-10 organizing worker's unions (can't find the link, but I know I've seen it in a documentary, with kids working by the age of 8 and killed by their employers,
http://www.labourfile.org/labourfile/lf_2000/Movement2.htm, it isn't far fetched) it and trying to secure better pay for their work. In India children are very young when they start to work, and their punishments are very harsh if they don't do their best (
http://www.frontlineonnet.com/fl1825/18250460.htm a lakh is 100 000, btw, if you care to read the article). Of course, this is slavery.
Actually, some of these kids think that it shouldn't be forbidden for kids to work, but that they should have better pay. You'll find that in some cases the kids are the only worker's in a family, because their parents can't get a job (
http://www.churchworldservice.org/FactsHaveFaces/childwrk.html). And this happened in the US just 100 yrs ago as well
http://www.eyewitnesstohistory.com/hnintro.htm - most of the kids in the pictures were at least 12, though a couple were as young as 7. But even today children work hard in the US, especially illegal immigrants (
http://www.gseu.org.uk/projects/childlab.htm)
As for war. There are pretty young kids in "armies" in africa. They are the most feared warriors, because they don't have any inhibitions with regards to what they'll do and to whom. Sure, some of that comes from drug use.
Apprenticeships in the middle-ages started in the early teens, and sometimes younger. Servitude could start as early as 11-12 yrs old. So again we're well ahead of the rules.
Then there are street kids around the world. They can act as thiefs, as beggars, as guides, you get the picture. Of course they are immature, childish, but they have some "street smarts".
All of the kids would much more like to play, go to school etc. Probably dream of a "Castle in the Sky" as Cosette sings in the musical version of Les Miserables.
Therefore, I as a DM allow most ages as long as there is a good story in it. With an eye to what children have done in history and even today, I'm also careful about categorically saying that kids can't or don't do that. Yes, they have limited wisdom, limited strength and constitution. But they might have very high intelligence, dexterity and certainly charisma.
All the links above comes from websearches I did while writing this reply; I can't vouch for each resource individually, but they are in line with what I've heard from other sources. That it seems a bit politic (a lot of unions in the above articles, not healthy family fun for American's I know, being unionized, I mean, almost as bad as being a socialist) shouldn't obscure the fact that there is more to children than the dismissal in D&D.
There is a lot of things which are swept under the carpet in D&D manuals, the broadness of audience is the reason for this, I guess. How gritty, how real you want your world is entirely up to you, though. I just wanted to show that young children can be pushed around by circumstances, and that young PCs would make sense in many settings.