The use of the verb "assigned" implies it's purely arbitrary, It isn't arbitrary. There are some cases of children born with mixed sex organs, but they are clearly abnormal. Their existence is not an excuse to obscure the fact that sex exists before it's discovered. It isn't assigned arbitrarily.
That phrase, “sex assigned at birth”, is dangerously inaccurate.
Sex can be discovered through a blood test (using mom’s blood) even before the baby is developed enough for sex organs to show in an ultrasound. Your sex is hardwired into you from the very beginning.