You are making a point I did not argue against. When the gender is likely to be female, use "she". When the gender is not knowable, use "he". There are contexts where "he or she" is clearer than simply "he" but they are rare. Typically, "he or she" is liberal-feminist newspeak.
Using "she" when the gender is likely to be female, and "he" when unknowable might have been ok when 99% of all nurses and midwives were female, and 99% of all doctors and engineers were male, but that is no longer the case. It doesn't matter whether you approve or disapprove of that social change, the fact is that the old times are not coming back. Here and now using gender-specific pronouns with reference to gender-neutral titles is becoming increasingly bothersome, confusing and embarrassing. Using the gender-neutral plural pronoun very neatly gets round the difficulty, even if it is strictly grammatically incorrect. It certainly seems to be the way modern English is going. I'd rather that than saying "he or she" and "him or her" all the time, that's for sure.