A groups only version would be good, yes, if only for coordination in a firefight.
The only real downside I see to removing this is that there are some police that actually use the message thing a lot.
Personally this set-message command has always been something that bugged me, especially when people just fire off two of those and fire.
Ever consider making set-message commands come up in a different color of text, that way people know whey they are being addressed with prerecorded messages?
IE:
Smuggler.McBob: Hey NY!
LPI-Bilbo.Baggins: Attention Smuggler.McBob, cut your engines at once and hold position for a scan!
Smugger.McBob: Oh snap!