1. Average speed is a useful measure for estimating your arrival time.
2. It's a simpler calculation (see other answers).
3. It is possible to estimate the effort involved in a ride, taking into account the elevation gained. See http://cycleseven.org/effect-of-hills-on-cycling-effort
4. Most competitive cycling sees winners as those who completed the course in the shortest time, which is related to average speed - distance/time. If you're going up and down the same large hill, it might take 30 minutes to climb and 5 minutes to descend. In terms of doing it in the shortest time, improving your climbing speed by 10% is going to make more difference than improving your descending speed by the same amount, saving 6 mins instead of 1 minute.

You can only accurately compare cyclists on the same course in the same conditions. Even then you'll find that some cyclists will be faster on a hilly course while others are faster on a flat course.

1. Average speed is a useful measure for estimating your arrival time.
2. It's a simpler calculation (see other answers).
3. It is possible to estimate the effort involved in a ride, taking into account the elevation gained. See http://www.cptips.com/formul2.htm
4. Most competitive cycling sees winners as those who completed the course in the shortest time, which is related to average speed - distance/time. If you're going up and down the same large hill, it might take 30 minutes to climb and 5 minutes to descend. In terms of doing it in the shortest time, improving your climbing speed by 10% is going to make more difference than improving your descending speed by the same amount, saving 6 mins instead of 1 minute.

You can only accurately compare cyclists on the same course in the same conditions. Even then you'll find that some cyclists will be faster on a hilly course while others are faster on a flat course.