> "She is a nurse" is also not a bias. It's a prior ...

Assuming that lower-status professions are female and higher-status professions are male ("he is a doctor") when translating ungendered words is indeed a bias.

> the system will be right 93% of the time.

And "this person is a doctor, that person is a nurse" will be right 100% of the time.

It's a bias in the sense that it accurately reflects a fact you dislike. It's not a bias in the statistical sense, namely something that causes the answer to be wrong systematically in a particular direction. See my other post here discussing the distinction.

It's also not wrong in the sense of generics: https://sites.ualberta.ca/~francisp/papers/GenericsIntro.pdf

The phrase "this person is a doctor" has a different meaning than "she is a doctor" - "she" and "he" refers to (I'm probably messing up the terminology here) contextually implicit person. "This person" does not.

> And "this person is a doctor, that person is a nurse" will be right 100% of the time.

Except when it produces "that person is a fine ship" or "John is that person's own person" or equally ridiculous things.