In the USA, all sales taxes on your item added together are usually just a few percent. (Higher in expensive cities though)
The only thing that is not shown up on the shelf is the deposit for beer & soda/water bottles that some countries have (usually around €0.10-0.20 that you get back when you return the bottle).
As a consequence, the sales tax rules are extremely local and the combination of all separate tax authorities that have jurisdiction over a specific retail location. While it might be nice if the sales tax was built into the price, it is a continuously moving target and therefore is simpler to compute on demand rather than physically repricing things on the shelves.
Still, seems like the retailer is in a better position to handle that complexity than the consumer. Surely it's better to have the retailer advertise the post-tax price (and occasionally lose money if they wrote the price tag assuming one set of taxes, and determined a different one applied at checkout) than for the customer not to know whether the $30 item they are buying is $32 or $38. It's not even that important that the customer's receipt correctly itemizes the taxes - that's nice, but it matters more that the retailer pays the right amount to the tax collector at the end of the year.
Also, "thousands of overlapping sales tax authorities" overstates the complexity. A typical retail location (the level at which price tags are usually decided) deals with 0-3.
Any sales tax decrease will not be transferred to the customer except in a delayed fashion under your model. Furthermore, requiring the retailer to eat any downside on sales tax changes will cause average prices to increase, albeit slightly in most cases, to transfer the risk to the customer as happens in every other market where operating costs are not directly chargeable.
And don't forget, the whole Europe still can't solve that for the last 40 years!
Wait...
They did.
Now I listening for the list of excuses why this country can't do the thing the whole world did eons ago.
... much like a retail store, where their overheads (e.g. the rent of the store) are also built into the price.