I find it strange not using a simple cycle computer. I see it as driving a car with a broken speedo. I only glance at it occasionally but I like to know it's there. It is also of great benefit when following a route that gives directions in distance (after 200 meters turn right.....)
Driving a car with a broken speedo is illegal and you could end up breaking the speed limit. Cycling without a speedo is perfectly legal and you can't break the speed limit except in certain rare conditions.
I just found that I ended up watching my speedo and whether my speed was higher/lower than average/last time leading to me competing with myself. Now I'm going as fast as I'm going and I just listen to my body telling whether the effort I'm putting in is just right or not.