sure we do - because that determines the distance a tire will cover in one revolution between one point on the outside of the tire and that same point again.

You're right - it's not a circle. And that's why the radius/diameters don't matter anymore. A square has a circumference, for what it's worth (technically, it has to be a closed curve - and the sharp corners make a square not a curve, but shapes other than a circle have a circumference, so the example works, and in the case of the square the outside perimeter is equivalent to the circumference). And it can rotate. The distance covered if it does one rotation and doesn't slip is circumference times rotations (n this case, one). That's a relationship that holds for simple 2 dimensional shapes with an area. Like our tire under deflection.

JB

PS - you're confusing the impact of inflating the tire (which most definitely can stretch the rubber) and weighting it down (which I'm arguing doesn't, at least not enough to matter in the real world). You also are consistently using radius when we have a non-round shape. Doesn't work anymore.