Personally as a instructor i have no problem with children getting certified. If they are able to pass the academic exams / confined and open water skills im more then happy to certify them. If they cant they dont get certified just like any adult.
The question should be is a parent / legal guardian qualified enough to take responsibilty for themselves and a child underwater. Ive seen many adults who can barely take responsibilty ie: sticking with your buddy, monitoring your buddies air, etc. for there buddy let alone a child.
Not to mention there is no requirement for the supervising adult to know how to even rescue someone in need of help. Personally i think there should be requirements of the adult supervising the child.
Just remember that diving just like anything else can be dangerious, snow skiing, water skiing, driving in a car, etc and we dont put all these requirements on them for children, Statistically diving is very safe if we follow the rules.