But I think this gets to the root of the problem. Text with generic pronouns can get clumsy , especially so if the grammar is less than perfect.
"He" or "She" removes any ambiguity that you are referring to a singular person. Whereas "they" could mean a single person, a group of people or some inanimate object. So a gendered pronoun can make your writing clearer but of course forces you into a specific gender.
Historically "He" was often used as a pronoun which could be considered either gendered or gender neutral dependent upon context.