That's interesting, but obviously, it's also a case where a plurality is implied. The speaker has a group of men in mind and doesn't know which of them she's talking about. There is an uncertainty involved, but it can't be about the sex of the person, as you note yourself.
I'm pretty sure you're confused about what "plural" means. Consider all the following situations:
1. "Everybody should bring their own books to class".
2. "If anybody has left their book at home, they should ask the teacher to borrow one."
3. "Can the person who left their book at their desk please collect it at reception."
4. "Someone has written to say that they left their book at their desk."
5. "The author shows their bias here."
6. "Joanna has written to say that they left their book at their desk."
Gramatically speaking, none of these are plural. In the case of #1, there are many people involved, but it "resolves" down to individual actions, since each person has a separate book. In #2 it's an indefinite number of people -- it could be 0 or 1 or 50; but again, it "resolves" down to an individual and that person's actions. In #3-6, it's clearly one specific person, with various degrees of uncertainty about who that person might be or what that person is like. In all cases except #6, you can replace "their" with "his or her", which was the prescribed way of writing this in my grammar classes.
I'll grant you that #6, where you refer to a specific known person as "they/them/their", is new. But #5, which is what we're talking about here, 1) sounds perfectly natural to me as a native English speaker, 2) was the sort of thing the grammar classes explicitly taught against, 3) is a natural extension of 1-4.
> Gramatically speaking, none of these are plural.
But even you used a plural, by saying "books" in #1, demonstrating that even when coming up with this example, you did not "resolve" anything just because "everybody" is a singular pronoun. You used "they" not referring to the word, but to what the word logically implied, and thus this "they" is also plural.
I simply don't see this natural progression that you claim. I see distinct usages of "they" for two different types of indefiniteness: one of number, and one of sex. #1-#3 show the first type. It's old and uncontroversial. (You seem to place #3 differently, but as written, the speaker cannot know whether the owner of the book and the owner of the desk are identical, or two persons.)
But #4-#6 don't exhibit any numerical indefiniteness. Here the "they" is clearly singular. It's my understanding that this usage is novel and did not arise naturally, but is the result of a political campaign, starting about 1960. That's why I asked for older historical examples, which could disprove this theory.
