The height from the road to the center of the wheel is NOT the radius. The radius it the distance from the center of a circle to the edge, not from the center of a circle to a flat spot on it.
Since you are familiar with heavy equipment, you should have a passing familiarity with track vehicles. Does the radius of the drive wheels change the circumference of the track? Or should I say length of the track. Where the tire meets the road, it flattens out a little, but the circumference doesn’t change, unless the tire pressure is changed drastically, but not for normal variations in pressure.
Road grader tires have a rounded tread, like a motorcycle tire. With a rounded tread, the tires circumference does change with the tires angle. Motorcycles steer by leaning and nor by turning the handlebars (at least not much turning). Car tires have a flat tread, they are not meant to be leaned. A tires camber does change when the wheel is turned, but that is to compensate for body lean and tire roll.