As AyrTC says, we do it because we are told to do it. I'd be more than happy to omit the numbers. If you are on the wrong code it is pretty obvious as the displayed callsign will be wrong.
I think it harks back to the days of manual input of Mode A codes into the Scottish Systems Radars. Well, we still have crap radar displays but at least these days they are linked up to the great God that is the NAS computer.
Perhaps you could get your ops guys to take it up with our ops guys and drag us kicking and screaming into the twenty first century.