And that situation is only when describing a generic, non-specific character with no major description. So only in the situation when the character not only isn't known, but doesn't matter. Something like Villager A.
You are correct that they are most often used as generics, esp. to describe groups of mixed gender or for instances where "he/she" would apply, in the same way that man is used to mean mankind as opposed to just men, but genderless he was used by Swift, Dickens, and Austen. Much of the usage will be found in academia (but what do they know
) especially by grammarians (who criticised singular they for requiring pluralised verbs and that it couldn't be used with "is": "He is", "She is", "They
is", and tried to force English to work like Latin) - most famous of these grammarians would probably be Anne Fisher (why she advocated for "he" and not "she" I do not know).
Just for perspective both Dickens and Austen also used singular they, along with Chaucer and Shakespeare (although Shakespeare also used "it" as a pronoun for a person at least once).
Another example is RPG Rulebooks which used he as genderless (some provide an insert explaining this). Due to the push back over the years on using he as genderless by those who said that it led readers to think GM roles were for men only has led to some now using she (or alternating she with he) as genderless.
Edit: Someone mentioned to me that the American authors Ann Leckie (used genderless he) and Seth Godin (used she as genderless pronoun in one and alternated usage of he and she in another book), but I haven't read their works so can't confirm.
Sidenote (off-topic? as this discussion was about the use of
her identifying gender): English also includes the un-gendered singular pronoun "One" (which was often used to refer to one's self rather than an other - so could cause misunderstandings) that has also been used as generic for groups - there is some stigma for using one as a pronoun due to social class-ism (perceived education levels) and it forces one to start referring to one as one throughout one's speech
.