If I was entitled to cycle in the middle of a carriageway I would be happy to monitor my speedo. Unfortunately I have to cycle near the kerb and I don't have the time/space to take my eyes off the road to do so.
That sounds awfully similar to the argument that it's simply impossible for motorists to obey speed limits as to do so would entail gazing rigidly at their speedometer, to the exclusion of any observation of the road.
Personally when I'm driving I find little trouble looking at several things in rapid succession - road ahead, mirror, road ahead, other mirror, road ahead, speedo, road ahead again (you get the idea ...) and modifying my speed and direction according to this stream of visual inputs.
I think it's a shame you don't feel you have the cognitive abilities to do something similar while cycling, and wonder whether or not you feel able to trust yourself in charge of a motor vehicle.