In my opinion, children cannot attain the same ability a black belt typically denotes an adult has. Regarding maturity, I've seen 10 year olds who were more mature than 30 year olds so I don't think that's an automatic issue. I've trained kids who were about 7 or 8 years old, but that was rare and he was initially limited by his ability to focus. Once he learned the basic routine, that 7 or 8 year old (I forget exactly how old he was) became the most mature student in the class. It depends upon the individual. I don't think you can set an age-limit and have it be 100% correct, but I think you can get fairly close. 18 seems like an ok age to me, if I had to pick one. Of course, now that I'm approaching 30, 18 year olds seem like children to me, though I swear I was WAY more mature than most of them when I was but 15
Then again, maybe that wasn't as correct as it felt like it was at the time.
ps-I'd just like to add that ultimately it should all be based upon performance of the criteria. I do think attitude is a big part of an Aikido shodan and it's very rare that young adults demonstrate what I personally consider to be a truly mature attitude. I'd say one good marker of a healthy attitude can be summed up like this: if one is ever more concerned with getting a blackbelt than simply learning and practicing then I don't think that person is deserving of the title. Rank is superfluous to the training itself and that should be understood before one reaches the "first step" that is shodan...in my rookie opinion anyway.