There may be advantages, for those insisting their mind won't accept reality and want to mimic the other sex all their life, from delaying puberty; but at the very least, it isn't the medical profession's duty to bully them into not having the treatment. Younger folk have parents or guardians to make the decisions.
However it's questionable that this is the sort of thing that should be on the NHS budget. You want life changing cosmetic procedures, go get a bank loan to fund it, and take responsibility. The NHS have plenty of life threatening or quality of life stuff to fund as it is, without allocating urgently needed money into such desires.