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I assume you mean proportional–integral–derivative control. https://en.wikipedia.org/wiki/PID_controller

The useful insight is not "compare desired state to actual state"; it's deciding which state to control

No, the bicycle is unstable. PID doesn't work well there.

In addition, it is controlling a coupled 3D system (which is unstable). This is much more than 3 PID controllers.

PID works fine if you parametrise it right, which is what this paper does. Consider the variety of inverted pendulums etc. that are used as as examples to teach PID control.

Bicycles are stable. In fact you need zero neurons to run a bicycle, all it needs is "power" and a large enough circle to run in.

If you can't use a PID for unstable things, why does cruise control exist for motorcycles?

> No, the bicycle is unstable. PID doesn't work well there.

This is just totally wrong. Stabilizing an unstable system is usually the first goal of controller design. Different systems do require different controllers, but pid is _very often_ perfectly adequate. It’s probably the most used controller structure in general.