Yeah, I agree that having a count-down for the light change is a bad idea. It would be better to have a count-down on the green and yellow lights. When a light changes to green, I always pause and look both ways to make sure someone isn't going to run the red (a practice that has saved me from more than a couple of accidents).
Insofar as road rage is concerned, in my experience this is almost always caused by inconsiderate drivers. People who change lanes suddenly without signaling, people who merge onto the highway travelling 35MPH, people who change lanes into the far right lane at a stop light just because it's open but who are not turning right--meanwhile a line of cars forms behind that car who would have liked to take advantage of the green arrow, people who get on a multi-lane highway and don't yield the far left lane to vehicles wishing to pass, etc. This far from a comprehensive list. The point being that road-rage would probably be a very rare occurence if drivers were more considerate of others on the road.