Evolutionarily speaking, having an internal sense of your own sex is important for a number of different mating behaviors.

"having a idea in your head of what kind of body you should have".

Transactivists LOVE to shift words around and then too often even people who are gc will repeat those phrases instead of thinking critically. When people have a idea in their head of what kind of body they should have, and their idea doesn't match the material reality of their actual body, we used to call that mental illness. To call it an "internal sense of sex identity" is just using their propaganda.

Also, in cases were intersex people were reassigned sex at birth, there is an extremely large number of people who end up rejecting their assigned sex and identifying with their biological sex.

In pretty much every case where an intersex baby was "assigned a sex at birth", the baby was a male DSD with abnormal genitalia and was then "assigned" to be female because the doctors figured it was 'easier to make a hole than a pole'. So it shouldn't surprise any of us when that kid grows up, realizes how badly women are treated compared to men -- and then "decides" they'd rather be in the more privileged class.

Which is why I must politely disagree with your belief that there is an element of biological hard coding regarding one's sense of sex identity. Unfortunately, that is exactly what transactivists say.