I track my sleep for the same reason many people track exercise, diet, habits, etc.: To encourage myself towards healthier lifestyle choices. Some of us will never improve what we don't measure. Maybe it just depends on how your brain is wired for this kind of stuff.
I know I need to get more sleep. I used to try to force myself to be in bed by 10:00pm. For some reason I just couldn't make myself do it until I started tracking my sleep. When you see metrics on your weekly or monthly sleep average, it just drives the point home and it gives you a goal to shoot for. It has helped me increase my average weeknight sleep from just over 5 hours to 6 hours and 20 minutes. I still need to get to 7 or more, but hey.. at least I'm making progress.
I have also used sleep tracking to figure out how much of my sleep was being disrupted. We used to have an old dog (bless her heart... I’d be happy to lose sleep for another year with her) who had to be let out during the night. Some nights that would cost me an hour or more of sleep in the middle of the night because I'd have trouble falling back asleep. My wife didn't believe it was costing me that much until I showed her the metrics. Unfortunately for me I was the light sleeper who always woke up, but I started poking my wife some nights to help so I could fall back asleep without getting out of bed.
Overall I see the sleep tracking metrics align with how I feel in general. When I am getting enough sleep and exercise, I feel much better. When I go through a week or two of not feeling well, it's often because I have been getting less sleep than usual. Do I need to be tracking my sleep to understand that more sleep = better mood, better health, and more productivity? Not really, but tracking it does help me remember to make better choices that lead to more sleep. It reminds me to avoid what comes naturally to me: Staying up late for no particular reason.