This in no way answers your question, BG, since I don't have children who dive. However, I do see quite a few kids diving and that's good....AS LONG AS it's done in the proper format. What makes me uneasy is when I see parents "groom" their kids as potential dive partners WITHOUT taking other measures. Some of those measures are to realize that when a great, big adult (usually male) goes diving with a child, the adult is essentially diving solo but with a young "charge" that must be looked after (I have a tendency to call them "ramoras", and that's not derogatory). That means the adult must have certain gear, training, guidelines and the responsibility to dive as a solo with additional duties. This will raise a few folks' hackles, so let me interject this to qualify the point. Children may very well have the mental and psychological readiness to dive. That does not make them an adequate dive partner. There are simply some physical and mental "equipment" they may not have yet developed.
The easiest comparison could be to rock climbing. I have been a BSA scoutmaster and have witness many young people in a myriad of situations. Occassionally, we would sometimes take the guys rappelling. Certainly, we worked safely and each youngster knew how to belay, arrest their partner's falls, etc... Does that mean I would want every one of them to belay ME? While the equipment can and does give a person of slight build some advantage, it doesn't mean it's safe for an 80 pound child to hold the lifeline of a 200 pound dad. There is simply too much at stake. Physical limitations would jeopardize not only the adult on the line, but also the young person on the other end. It's the same way with diving.
You are wise to objectively scrutinize your children and evaluate their readiness to dive. You are correct in realizing that it is, indeed, dependent upon the individual child. When parents get into trouble is when they overestimate their child's abilities and limitations.