It makes sense to those who used to spod for hours on Ewe-Too talkers, Circle, Rom, and Diku MUDs, several MOOs and MUSHes, and all of the chat systems and games inspired by them.
If you're going to argue for grammatical correctness, it should probably be /i although that could lead to disagreement in the verbs once the 'i' is replaced by the person's name. I guess '/acountname yawns.' would make sense, but getting the code to allow for each monk's own name and getting people to type their own nickname instead of '/me' is more work than just aliasing '/em' to '/me'.
It's not like '/msg jdporter hey, how are you?' makes sense as anything other than a command to the system, either. I'm not sure why there's such a focus on making '/me' or '/em' fit better into conversation than that.