At all but very slow speeds, a car doesn’t change direction by rolling along the arcs described by the front wheels. For the car to change direction there needs to be an external force applied (see Newtons Laws of Motion). When the wheels are turned the tyres scrub across the ground in the direction of travel- it’s the reaction to this that supplies the force to change the cars direction. The greater the angle or speed the greater the force. If you don’t believe this, try changing direction on a sheet of ice. That’s why when you are going quickly you don’t need as much steering angle. It’s also why Ackerman isn’t as important as you might think, except to stop you ripping tyres to bits while parking.
Alan Fairless