If people are born trans it reinforces the born in wrong body theory, and lends weight to the importance of modifying the body to fit the mind rather than vice versa.
I wouldn't say so. It is perfectly possible for someone to be born with brain damage that causes them to not have a correct "map" of their bodies in the brain. That still doesn't mean the body is wrong.
I once read about a study that the children born to women who had been given a specific medication that influenced hormones, were about ten times as likely to be trans-identified as adults, and some had mutated genitals.
So there's possibly a biological element. Which still doesn't mean that the body is wrong (well, unless the genitals are mutated, that is) but that the brain is damaged.
Common sense would suggest to first try changing the mind to fit the body, via psychotherapy and medication, and only then to even consider modifying the body.
Brain surgery is still very dangerous, but considering that there's so much progress and I recently read about a treatment that allegedly can cure depression surgically, that might become an option in the future.
Anyone with any common sense will see that modifying the brain to fit the body is the preferred method if the body is perfectly healthy; as science is not currently able to create reproductive organs, and that while not all humans want to reproduce, at least women need the hormones produced by their reproductive organs to remain healthy.
Gender dysphoria that kicks in during puberty is just that; gender dysphoria, not sex dysphoria.
I felt very uncomfortable during puberty and if I could have the body of an 8 year old female child, only taller and stronger, I might quite like that. That doesn't mean I am transsexual, it means that I hate the feminine gender role (and also menstruations are a pain).
The solution to that is the liberation of women from patriarchy, and adequate compensation for the pain of menstruation (think free chocolate). Not massively harmful surgery and artificial hormones.