My big question is, WHY is average speed such a horrible metric to use? If I shouldn't be monitoring my speed, what IS a good metric to monitor?

I understand that average speed will change depending on route/terrain/etc., but I figure it's a good enough way to tell if I'm getting better. For example, before my first triathlon this past weekend, I rode the tri bike route a couple times a week. When I started, my average speed was 15-16mph, and at the race my speed was 17.2. Probably a good indicator that I am getting better, right?
My computer doesn't include time stopped in average speed, but I really only care about my speed when I'm moving. I can just look at a clock if I'm curious about how long the ride actually took (as opposed to the ride time my computer shows me, which stops timing when I'm stopped).