As to your first point about someone changing their gender to be cool as a teenager, there is a big difference between allowing gender affirming care and actual transition to a different gender. I think most people including the medical profession don't think a child should be able to have surgical procedures to transition until they are legal age. Puberty blockers are reversible so I believe parents should be able to decide with doctors whether or not their child should take them.
As for your second question, there is a difference between being content with your situation and being truly happy. Older people have families, friends, parents, co workers, jobs, etc. that would be impacted by their decision to come out. Their whole lives would change. Some people are willing to take the risk while many probably are afraid of the consequences. Keep in mind older people have older parents who are more likely to be uncomfortable with the idea of a gay son or daughter.