The question is, in reality, about what business model a dive op is using. If the dive op wants to cater to kids, and is competent and experienced and set up to do so, then it should work just fine. If not, it won't.
We operate a horse riding school in San Diego, and there are lots of parents and kids of all ages here. We welcome them and teach kids as young as 4 or 5 to ride. Many of those kids continue riding with us until they go off to college, and sometimes they bring their young children back to us to learn to ride.
Are there dangers? Yes. Are there special needs? Definitely. Do we require parents to supervise young children at all times? You betcha. It is not unusual for kids to have allergies, learning disabilities, illnesses, etc. etc. and you need to know how to recognize and handle these things.
If there are enough folks with young children who want to take them diving, some business will make that their specialty and set themselves up to do it properly. But those that have not, shouldn't be expected to become babysitters without prior notice and agreement.