Actually, I recently read an article by Khosroshahi which included a study demonstrating that "his/her" does not in fact carry a gender bias -- people who use "his/her" in writing were likely to assign a person described without gender terms their own gender, cf. people who use a single gender generically (i.e. "his"), who were more likely to assign a person that gender.
Assuming that because "his" is listed before "her" there is a gender bias is taking things way too far - since language is a linear medium, you have to pick one to be in front, and I think most people understand that it's not trying to give the choices an inherent order.
Your first paragraph relates to another study that Wikipedia cites: "a study by John Gastil found that while the plural 'they' functions as a generic pronoun for both males and females, males may comprehend 'he/she' in a manner similar to he."
"his/her" is a bit of a bugbear of mine in any case, not only for the ordering, but because it lacks cosmetic elegance. "They" is an ideal alternative.
It is interesting to note that in most figures of speech, the male variant is listed first. For example, "his and hers", "Mr and Mrs", "he and she", "his/her", "Lords and Ladies". Yet, "ladies and gentleman" is a popular counterexample. Funny stuff this English language! ;-)
Assuming that because "his" is listed before "her" there is a gender bias is taking things way too far - since language is a linear medium, you have to pick one to be in front, and I think most people understand that it's not trying to give the choices an inherent order.