In KKW taekwondo, a first dan/pum represents completing the beginner's course. In Korea, it takes one year to get to first dan/pum.
Given the wild variance in the maturity exhibited by adult black belts of varying arts, I don't view maturity, leadership or responsibility as being anywhere near a universal requirement across arts. Some of those most vociferous about this on MT spew the most vitriolic and hateful posts using the language of a middle schooler while claiming to hold instructor level (fourth dan +) grades. Also, many who insist on maturity and leadership in a black belt generally are fine with eighteen year olds receiving them. Eighteen - twenty two year olds are not generally known for their maturity.
In fact, this is the age of reveling in greater freedom and engaging in all manner of irresponsible behavior before settling into a more adult role. It is the time of making mistakes and learning from them first hand as a legal adult. I've seen a lot of kids who are actually very mature between twelve and fifteen who seem to regress between sixteen and twenty, but begin to pull it back together in their early twenties. This is because the maturity that they had from twelve to fifteen was partly imposed upon them by their parents and teachers. In their mid teens, kids frequently start pulling away from authority figures and try to establish identities of their own. They begin to question authority more, and it usually takes them into their mid twenties before they have a maturity that is truly their own.
High school athletes (this includes MA students) can put on an air of maturity, and in the context of their given sport, be the comparatively mature leader that we associate with a black belt. But once off of the field or out of the studio, they usually go back to being high school kids. Which is what they're supposed to be doing.
Once they mature, they may stick with a martial art or a sport and develop true maturity both in the studio and out. Most kids in MA programs do what most other high school students do: go to college, the armed forces, or into a trade and stop practicing the art. A few will come back to it later in life, but for most, their time in the arts is looked back on fondly but is a part of their youth and unlikely to be revisited. Only a very, very small percentage will actually stick with an art from childhood through college and become a lifetime practitioner.
So when the insistence on a black belt somehow meaning "more than physical skills" is made, I think people are thinking more in the ideal than the actual. It may be true in some schools, and perhaps in yours. But I caution against applying such a standard across all arts, schools and practitioners.