I swear that this was suggested recently, but I can't find anything.
I don't think that private messaging would be very good for the site. It'd probably cause unnecessary drama at some point, and there's no way we can moderate it. A decent portion of the users here are younger, and while I'm not someone to be all like "predators are everywhere on the internet!!!!!! strangers are all dangerous!!!!", but things like that do happen, and adding a private messaging system would make that a possibility here, where, without it, if we see anything strange going on, we can quickly deal with it. This is a Pokemon forum website, there shouldn't really be much of a need to discuss anything privately. Using something made specifically for messaging, like Discord or Hangouts, would be a much better experience, anyway.