Logging and nick registration are both extra services that run ontop of IRC. At one point I extended an IRC server where you could send a list of regex filters

Logging and nick registration are both extra services that run ontop of IRC. At one point I extended an IRC server where you could send a list of regex filters. When messages where sent to channels you had joined that matched the filters it would send you push notifications. I think that combined with logging is really all people want on mobile. Unfortunately someone has to actually run the push server and that 1) Requires more work than volunteers are willing to do 2) Can only be done by people holding the certificates used to publish the app. I've personally just given up on popular mobile OSes. They're a disaster in nearly every way.