Why aren't average speeds computed over distance?
This is an interesting point of view. Let's unpack this a bit.  

Assume I have a ride that is 10 miles of flat, 10 miles of ascent, and 10 miles of descent.
On the flat I maintain a constant 20 miles/hour.
On the ascent I fall back to a constant 10 miles/hour.
On the descent I maintain a constant 30 miles/hour.

My average speed for this would be:
(10 miles + 10 miles + 10 miles) / (0.5 hour + 1.0 hour + .33 hour) = 16.39 miles/hour

By the proposed calculation I would have:
(100 tenths/mile * 20 miles/hour + 100 tenths/mile * 10 miles/hour + 100 tenths/mile * 30 miles/hour) / 300 tenths/mile = 20 miles/hour

If I had an average of 20 mph I should be able to complete the course in 1.5 hours.  The trouble is that the course would actually take 1.83 hours to complete at the actual average of 16.39 mph.  I know it hardly seems fair, since by all rights you did the vast majority of miles at 20+ mph.  The caveat is that you spent by far the greatest amount of time at 10 mph.