Once you have a path to follow, classical control theory can be used to control the steering angle to follow it.

But classical control theory hasn't been able to extract, from camera pixels, the open path in a road with cars, bicycles, and pedestrians. Camera inputs are million-dimensional, and there aren't accurate theoretical models for them.

Unmanned drones are orders of magnitude easier since you don't have anything that you can just fly into once you are above few hundred feets. They also don't have to rely on any vision based sensing. E.g. a drone has altitude, current speed, heading all of which while noisy can be represented easily as a small set of values.

The whole Lyapunov and control theory assumes perfect knowledge of sensors. Even though the signal itself might be error prone you have a signal. In case of autonomous driving even in simple cases as those described in the blogposts knowing the exact position of the markers and then using them to tune the contoller is not as easy as you might think.

The end-to-end system shown here solves three problems it processes the images to derive the signal, it then represents it optimally to the controller and then tunes the controller using provided training labels.

I cited Lyapunov, more as the ABC of nonlinear controls. Much more can be done in an analytical fashion, the "end-to-end" system here does not "solve" anything. It is a trained steering command regressor, nothing fancy, it's likely to work in this guy's living room, under certain lighting conditions, there is no way of predicting its accuracy, sensibility or anything else. Engineers have been breaking down systems into sub systems for a reason -> tractability of testing and improvement. End-to-end systems like that have close to zero value if you need something reliable.