Hmmm what about other "cosmetic" procedures that a baby or even a young child can't agree to. I'm thinking about raised raspberry marks or moles that don't cause any physical interference but that a doctor has suggested removing, or a dental cap for a non white tooth that is otherwise fine. I'm sure there's other such items too. Things that don't interfere with normal life but require a parental decision on a body modification that will most likely leave a mark.
Raised raspberry marks (hemangiomas) and moles can be indicative of serious medical issues... like skin cancer or other types of cancer. Kids can have these types of cancer. Saving a kid's life is more important in this scenario, which is a bigger decision to make and must be made by the parents. A doctor usually won't suggest removal of skin discoloration unless there is a medical issue. So far in my life, I have never heard of a parent putting their kid through cosmetic surgery without having a medical issue that supersedes the cosmetic issue.
My DD has a dime-size mole on the back of her leg. My father, who is a doctor, suggested we should get it removed. Not because it is medically necessary, but because he thinks it's unsightly. He can be a jerk sometimes. She is only 5. He mentioned it shortly after she was born. I declined and said unless there is a medical reason, we're not touching it. If my DD doesn't like it when she's older, we'll revisit our options. She can decide that one on her own. No unnecessary surgery in my house.
As for cosmetic dentistry on children, never heard of it. Do people do that??