I don't like the options that are usually given in the "gender-neutral pronoun" debate. The singular they offends my prescriptivist sensibilities. His/her constructions are clunky and look terrible. The generic he is simple and I find Strunk and White's (3rd edition, 1979) defense of it persuasive, but many these days consider it unacceptable. The generic she is still better to me than the singular they, but it seems retaliatory and besides has problems similar to those of the generic he.
I recently noticed a fourth option: use he and she as generic pronouns on an alternating basis. For example, if referring to a student, use she the first time. After completing the section of the discussion, referring to this imaginary student exclusively as she, the next paragraph or page introduces a second example student, and for this example the pronoun used is he.
The author intends that both examples be understood to refer to students of any gender, and carefully avoids gender stereotyping, such as regularly using "she" when referring to an art student and "he" when referring to a science student. The author also never switches the pronoun in the middle of an example.
This method has its drawbacks, of course, but I'd like to know if it has been recommended by any published style guides. If not recommended, has it been considered a viable option?
This question is different from the many others on this subject because a) I am asking about a gender-neutral option I have not seen discussed on ELU, and b) I am asking for style guides, not merely "is this acceptable?"