For a given class of goods Europe generally has one VAT rate for the whole country.

In the US the sales tax for a given in-person sale is the state sales tax, plus possibly county sales tax, city sales tax, and sometimes even special tax district sales tax.

For remote sales, it is similar except the tax is computed using the buyer's location rather than the seller's location.

If they can calculate the price at the tills, they can calculate the price for the labels on the shelves, or the price stickers

They can do that but that costs money so they never will. We worship the dollar like its a god above gods. No way we're going to willingly do something that costs the rich a dime more than absolutely necessary.

But they cannot calculate price on ads. Also, can you deduct VAT from your taxable income in Europe? Sales tax in the US is deductible.

VAT is deductible if the buyer is a VAT registered business. The amount of VAT is still printed on the receipt by law, so you can still know how much you pay.

Companies already manage seperate ads in the EU for language, currency and price discrimination reasons, it's really not a huge bother.

So customers cannot deduct VAT from their personal taxes... I also doubt that separate ads per township are common in EU. For example, in Los Angeles the city is made from several separate townships with different sales taxes, two shops on the same street may have different taxes because one can be in LA and another in Santa Monica.