Like you just about every golf cart I've ever seen hauled is strapped down this way. I've never heard of or seen one damaged from it, but I can see how it could happen if you got carried away.
You're correct. When the wheel design allows it, I go through the wheel and not around the tire (as do most haulers that use this style strap). I do this for a couple of different reasons. 1- It is a more secure way to tie-down the car, the strap can't come off and it's faster. 2- When you go around the tire instead of through the wheel you risk damaging the strap and anything on the backside of the tire (brake lines, abs sensors etc...)
The straps are not all that abrasive and don't rub (or move around on) the wheel while in transit. If it's a brand new vehicle or has really nice rims then I error on the side of caution and go around the tire to eliminate the risk of scratching the rims. So far (insert smiley knocking on wood here) I've never scratched a rim with the straps.
Thanks for asking
-Sam