"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.

You can't just drop a pronoun like "they" or "he" in without a previously-named referent (the way you could with "one" or "many"), so the kind of ambiguity you refer to here is almost never a problem in practice. Its only an issue which creates a difference between the two pronouns in the case where there a multiple named referents already to which the pronoun could be referring, and some are in the broader class that "they" can refer to but not in the class that "he" can refer to.