I agree there aren't any perfect solutions, but a reasonable solution is to go 1) if the user specifies, generally accept that (none of these providers will be willing to do so without some safeguards, but for the most part there are few compelling reasons not to), 2) if the user doesn't specify, priority one ought to be that it is consistent with history and setting, and only then do you aim for plausible diversity.

Ask for a nurse? There's no reason every nurse generated should be white, or a woman. In fact, unless you take the requestors location into account there's every reason why the nurse should be white far less than a majority of the time. If you ask for a "nurse in [specific location]", sure, adjust accordingly.

I want more diversity, and I want them to take it into account and correct for biases, but not when 1) users are asking for something specific, or 2) where it distorts history, because neither of those two helps either the case for diversity, or opposition to systemic racism.

Maybe they should also include explanations of assumptions in the output. "Since you did not state X, an assumption of Y because of [insert stat] has been implied" would be useful for a lot more than character ethnicity.