Former university English instructor here; the usage you are critiquing is widely regarded as a good tradeoff between deferring to the gendering baked into our language and recognizing the integration of a population.

It's often much easier to write and read pronouns, and it is my opinion (though far from an accepted truth) that alternating him/her when contextually appropriate is less clunky than using the him/herself construction.

As a writing instructor, I personally have no problem with "himself" being used in a broader, non-gendered construction... and for the same reason have no problem with a similar usage of "herself", though as I say, opinions vary.