I don't think the announcers should wrestle regularly, especially as jobbers. It would be a bit hypocritical to criticize a guy for losing from the announce booth when you are losing matches yourself on a regular basis. I think they need that seperation to be effective. However, I agree that they could be used in spots. Usually once or twice a year Lawler gets pulled into an issue that requires him to have a match or at least throw some punches. No reason Matthews and Striker couldn't do the same.
It actually puzzled me that of all the announcers that Daniel Bryan had an ongoing conflict with it was Cole. I know they are trying to get Cole over as a heel announcer but had it been Matthews or Striker that Daniel had friction with they could have actually faced each other in the ring.