This could be useful when you need to speak in private with a staff or a friend in the main chat box. The argument could be like !pm [steamname] "message". I've set up an example situation:
MY CHAT POINT OF VIEW-
12:45:03 Random Person: nahl badwater pls
12:45:09 icyfrenzy: !pm ninjaMooCow the leader of the upward lobby is trolling
12:45:10 TF2Center: [PRIVATE MESSAGE] ninjaMooCow has been notified about the private message.
12:45:28 TF2Center: [PRIVATE MESSAGE] ninjaMooCow --> you: ill look into it
NINJA'S CHAT POINT OF VIEW-
12:45:03 Random Person: nahl badwater pls
12:45:10 TF2Center: [PRIVATE MESSAGE] icyfrenzy --> you: the leader of the upward lobby is trolling
12:45:27 ninjaMooCow: !pm icyfrenzy ill look into it
12:45:28 TF2Center: [PRIVATE MESSAGE] icyfrenzy has been notified about the private message.
Of course the argument won't be visible to others. The only problem I could think is that some people are lazy to search up the SteamID of the person they want to private message.