The term “assigned” may be appropriate for a few intersex people, but certainly not the majority of humans, who aren’t even intersex. Would you say things dated using radiocarbon dating are assigned an age? Radiocarbon dating is probably less reliable than human sexing.
It’s more appropriate to say that sex is recorded at birth rather than assigned. But in most cases, you should speak of biological sex rather than sex assigned/recorded at birth or similar terms. Because that’s what really matters in most cases. Saying “sex assigned at birth” when you mean biological sex really seems like sugarcoating biological sex and like a euphemism.
By the way, David Reimer was actually recorded male at birth. It’s just that he was raised as a girl.