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