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.

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.

But in this case though, any kind of state space control also requires rather precise knowledge of the physical laws that govern the dynamics of the vehicles. When such information is not available, can neural nets do a decent job at mimicking an analytical control algorithm? I think that's an interesting problem worth exploring.