If the effective tax rate is 7.432%, you can price single items so that the price plus tax ends up in a multiple of $0.05, but if you get a purchase with multiple items, you either need to round somewhere or post prices that are like $9.346263437.
I know it's hard to imagine the price on the shelf being the price that you pay, but I believe it is possible even in complex tax situations.
But good luck convincing every state, county, municipality, and other weird governing body that requires something other than that and also collects a weird sales tax.
Or go with the solution that papers over all that nonsense: a flexible and maximum $0.04 per purchase discount.
I live in a place with a fixed VAT (that is included in the price on the shelf / menu / ...), but grew up in the US in several different weirdly taxed localities. It's just such a silly argument to say "we can't write the correct price on the shelf because the laws vary." The register knows the correct price, the labels on the shelf are computer generated, and updated regularly. The labels at many nation wide fast food type places are displays anyway.
If Baarle-Hertog and Baarle-Nassau can make it work I feel like it's at least imaginable that stores that already automate this weird complex tax code could print accurate labels instead of inaccurate labels, with an accurate calculation at sales time.
Most of this could be resolved by not putting the prices on the products themselves, but that isn't as good of an experience for the shopper.
That is already often the case. Prices are usually on the shelves not on the product itself at many stores. And when purchasing online there is no reason that the sales tax couldn't be included in the listed price.
Also sellers could just charge the same price everywhere and take the sales tax out of the revenue.