I wonder if this could encourage retailers to start advertising tax-inclusive prices. That way there's no rounding in the customer transaction (if they set all their tax-inclusive pricing at multiples of 5 cents), and then the sales tax would just be calculated in aggregate, and paid electronically with no rounding.
We had a coffee shop that tried to do it. Listed prices included taxes, and the total prices were in nice whole numbers (IE, $2 for a cup of coffee, $5 for a latter, $8 for a sandwich, etc.). But regulators stopped them and they had to go back to listing the prices without the sales tax.
It's frustrating how much needless friction gets put into the system.