Why are bicycles considered vehicles and not "walking aid"?
a cyclist has the speed, mass and maneuverability of a sprinting person


Not really! The world record for 100 m sprint is 9.58 s, which equals 37.6 km/h, which is fast but not anything spectacular for a bicycle. The marathon world record equals to little more than 20 km/h, which is less than my average commuting speed. Going back to "human" speeds, I would estimate that an average biker goes roughly twice the speed of an average runner.

With double speed:


Braking distance is quadrupled (ignoring reaction time).
Kinetic energy = damage in case is collision is quadrupled (not even taking into account 10-20 kg extra mass &amp; hard and sharp metal parts of the bike).