This has been a very serious topic in our area the past couple of years.
I agree with what has been said to this point. Most coaches don't know the mechanics of officiating and how a crew is supposed to work, what official has what responsibilities in different situations.
I also agree that coaches should have some input into a ratings system. Afterall, we are providing a service to the schools that hire us, but that input should be limited to things like how an official interacts during a game. Is the conduct professional? Did the official communicate when NECESSARY and as the game allowed, not to be confused with a question like "How could your partner miss that?" A coach can evaluate things like the ability of the referee to keep up. Although a tough criteria to evaluate, did the official have control of the game?
The biggest issue for coaches that I see, is how objective can they be when they are more affected by the result of each call. Jobs are on the line, depending on the level you coach at. Most coaches still pay more attention to what is happening near the ball, but officials must see on-ball and off-ball. Do you have a personal relationship with any official? If so, can you really be objective in their evaluation? Coaches really don't understand the concept that contact is not necessarily a foul. These are things that limit the effectiveness of using coaches in a rating system, but there is a place for them.
I know alot of people will have different thoughts on this. I wonder how coaches would feel if the officials were to evaluate coaches on their performance. Its seems like alot of coaches have never lost a game because of something they did (like got T'd or put the star back in the game with four fouls too early) or didn't do (go to a man-to-man), it was either a "player didn't get it done" or a "ref screwed me."
So many thoughts, so little time