This doctor obviously feels as strongly about WLS as you do - but in the opposite way. She mentioned being fed up at the number of patients coming back with complications - I don't think she would lie about that. She does not regard WLS as 'the answer' - this is her personal opinion as a trained medical professional, and a family doctor, and she is unwilling to recommend WLS surgery for your 17-year-old daughter. She's thinking of Emma's health and her future, I honestly believe. She knows what Emma will have to go through, and how hard it will be for her, afterwards, even if all goes swimmingly. I know that a refusal was not what you hoped for, but I do understand your GP's misgivings.
Emma is probably still growing. Any surgical procedure that might seriously limit her ability to absorb food, liquid and vital nutrients - for a period of months or even years, according to the many personal histories shared on this forum - might be harmful in so young a patient.
As angiemason observed recently - we don't like to be told no. I, myself, think that 17 is too young - a personal opinion, only. I wouldn't allow my child to have WLS at that age. But you must do what you think is right.
Good luck to you and especially to Emma x