That's all fine and dandy in theoretical world, but I'd dispute that the probability of a transaction resulting in value v is uniform. I'd guess that there's some fairly prominent banding due to psychogical pricing at or just under 'round' figures.
It's only America that seems to add it at the register. I assume it's to take advantage the famously high level of math education among Americans who can easily add 4.5% state and 1.8% city sales tax to a coffee in their head.