implying that there has to be some sort of gender-based polymorphism among pronouns.

Pronouns are a shortcut for a noun. They do not need to be linked to genders. Singular third-person pronouns benefit from some variance based what is talked about. As other comments pointed out, these third-person pronouns could be based on social status, age, physical proximity, familiarity, etc.

That's all there is about my question.