I agree that it's easier. Eventually "they" will probably replace "him/her." Language drift takes time, though, which was my original point.
My guess is that the initial response by MisterTea was an attempt at language policing, and this whole thread is a waste of time.
I think he/she will become outdated soon, if it's not already. I don't think anyone really anticipated there'd be a global debate about gender identity. Regardless of how anyone feels about that particular topic, it's not going to go away. Either everyone naturally shifts to the more inclusive "they" or people will continue to clamor for it.
Matt Levine's not alone in his use of "she/her" - it's actually fairly popular in modern technical writing, I've found.