I think each demographic would have a different set of answers to that, and even each person.
Overall, I think a person should certainly strive to lose weight naturally, if they can. If they cannot, for diagnosed reasons, then I think it would be appropriate.
I think the idea that doctors require you to be within a certain weight range before having the procedure is a great idea. I have a cousin that had to lose like 50 lbs before having the procedure and she didn't have any poor effects from it.
My mother, on the other hand, got it when she was almost 350 lbs (I don't remember her being really big though). She had Diabetes so that led to slower healing, but also there were several complications, not only with the procedure, but with her healing itself. Infections, long-term effects, and she still does not have a decent diet. Better than before by a lot though. And she is probably still around 250 lb.
So, it depends on the person and if they will be changing their diet. If you still eat the same foods, your weight will go back up once the band is removed. If you change your diet so it is healthier, then it will enhance the effects of the surgery. That is another benefit of the weight limit for the surgery, that many will have to change their diets for the better beforehand.
As for age, I think once you are 16, you should be allowed to have the surgery. People give high schoolers too little credit for their personal responsibility and awareness of their bodies, but I do think whoever is paying for the surgery (aka parents/guardians) should agree to it as well. The person choosing to have the surgery should be able to prove that they are capable of doing well for themselves and that the procedure would be enhanced by their actions.
TL;DR 16 years old should be the limit. There should be an acceptable weight range, but the person should prove they will live healthy to enhance the effects. Try to lose weight first, if that is not enough, then the procedure.
P.S. I am in a Dietetics degree program because I am particularly interested in weight loss as a profession, but not so much the medical side (which is why I am in Dietetics, not Bariatrics).