The reasoning I've always understood is that the width of the tire is the primary thing that determines how it fits onto the wheel (assuming it's the correct di

The reasoning I've always understood is that the width of the tire is the primary thing that determines how it fits onto the wheel (assuming it's the correct diameter), and that different tires due to different tread block designs have subtly different heights, but in a way that is negligible, so aspect ratio allows you to have a standardized understanding of height without being so exact as to be confusing. E.g. a consumer knows that they need either a 245/40 or a 255/40 for their 9" wide wheel, and that in either case their speedometer would be correct (which is based on total height), but brand A and brand B at 245/40 have a .3" difference in height. It does make things difficult for folks that slam their cars though when they don't want to rub, because there's less margin for error so they really need to measure the height of the tire.