I would absolutely wave a magic wand to have the shelf labels include tax. Long gone are the days of having to relabel literally every item when the tax rate changes, and the advent of digital shelf tags makes it trivial. I do see some differences with the 'tariff surcharge' from sales tax though:
* Sales tax is the same across vendors. I know the approximate sales tax in an area. I don't know via what exact supply chain the store obtained an item, or when, so I can't know what the tariff was. The store doesn't either -- individual items that were subject to differing tariffs are indistinguishable on the shelf, thus the tariff surcharge will be arbitrary.
* Companies hate to disclose what they paid for stock, and in many cases are contractually prohibited from doing so. An accurate tariff surcharge would disclose this to me. Thus the surcharge is going to be an approximate / averaged amount.
* Approximate surcharges become the dumping ground for 'whatever we think we can add at the end of the sale process that won't cause the customer to abandon their cart' with little relation to the actual cost to the company.
* I am not aware of a case where a store gets to keep some of the sales tax. If the tax rate goes down, they don't get to keep charging the higher rate and 'oopsie' keep the overage. A tariff surcharge, since it necessarily can't be linked to the specific unit, is really just unbundling their cost of goods sold so they can double-dip.