[snovv_crash]

As someone who's tried to control a car with PID, there is more to it than that. The angle of the car relative to the lines and the distance from the line need to be taken into account separately, since they each independently contribute to the distance from the lines as you move forward, and the PID controller can't separate them by itself. Think of how hard it is to keep straight in heavy fog when you can only see a few feet in front of the car, and you'll get the idea.

The delay in your steering response (how fast you can measure the error and turn the wheel) is large enough here that if you aren't actively taking the non-linearities of the problem into account you will oscillate off the road. The other way to fix this is to aim for a point far ahead of you such that your steering response time is significantly less than your "following distance", but that results in cutting corners.