>We have all the physics solved for bikes, it's a complicated system but so is everything in motion. Hence we assume a spherical cow for the sake of the problem.

This depends upon the question one is trying to answer. If one is trying to create a bicycle that can self balance, that involves considering different factors compared to trying to determine why certain injuries result in a person losing the ability to balance on a bicycle while others do not. Is the focus the bicycle or the human?