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.
The difference in diameter would be an 1/8". On a 27" tall tire that could mean a difference of almost 1/2" in the circumference. It’s debateable as to whether this would be harmful or not. On dry pavement, maybe; in the muck, probably not.
It seems to me that tire companies are using misleading information to sell tires. Every AWD has a differential or viscous coupling between the front and rear axles.The idea of all-wheel-drive is to drive both axles, but allow a difference in speed between the front and rear axles. This concept works by just adding a differential in the transfer-case which works exactly like a differential in an axle. If you didn’t already know, the purpose of a differential is to allow for differences in wheel speed, or in this case, differences in axle speed.
The argument advanced by tire retailers is that a difference in tread depth causes a difference in axle rotation that will damage the drive train. This overlooks the fact that every turn causes each tire to travel at a different speed. A difference of 2/32 tread depth (4/32 or 1/8 inch in diameter) causes of each rotation of a tire to travel an additional .39 inches. This would be an approximate difference of speed between the tires of 0.4 percent, with 20 inch wheels. To put this in prospective, during a slow turn with combined front axle length between tires of 60 inches the tires have about 0.4 % difference in speed in a turn of 1250 foot radius. (A VERY gentle turn). Every turn of less radius (for example, into your driveway) produces a far greater difference in tire speeds. Modern vehicles are made to accommodate modest differences in tire speeds. Thus the entire notion that a difference in tread depth will cause vehicle failure seems all hype to sell more tires. Unfortunately, this “common knowledge” keeps being repeated. Doubtless large differences, such as different sizes of tires on a vehicle might challenge the ability of the differential or viscous coupling to handle the difference in tire diameter.
This is just wrong. Differentials work for occasional difference in tire speed, not constant difference. You’ll ruin a viscous differential that way. It’s not the tire companies, it’s the makers, Subaru for example, that require closely-matched tires.
I’m not much of a believer in conspiracy theories. From my hazy memory I seem to recall that as far as Subaru goes there is a very slight ratio difference between front and rear differential. Not much at all but it’s factored in.