You can't pre-calculate the final taxed price using the local tax algorithms as they are today. They number can't be known until the transaction takes place.
In any case, I'm not saying that it can't be done, just that it may be a lot complicated than adding a fixed percentage to every price label.
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.
Companies already manage seperate ads in the EU for language, currency and price discrimination reasons, it's really not a huge bother.