I'm sorry, not trying to derail, but I genuinely don't understand! Does it not cause more issues if the person thinks their body is 'wrong'?
These people don't think their body is wrong, exactly. That's gender dysphoria, which is what surgical treatment was supposed to be a "cure", or at least a palliative for, if psychological treatment was ineffective.
These gender people are doing it more for more complex psychological reasons. The body modification is partly a ritual induction into a group, partly an assertion of control over the self, a whole bunch of things.
So it's not as inherently contradictory as it might seem.
Here's a take on the "ritual" part of the phenomenon I found interesting the other day, that I think has a lot of truth in it.
Gender Identity Isn't Real
Medical transition is ritual purification.
[...]
If those who are born Black or disabled are the chosen, trans people are the converts who have voluntarily accepted Marginalization. They choose to suffer more from their involuntary embodiment. Because of this, they become virtuous. They are saved.
Girls in particular have often had an urge to self-harm - cutting, bulimia - and this is an organised outlet leveraging that.
Very little connection to the prototypical 20th century dysphoric transsexual (usually male, very rare).