Technically, you’d have to declare what you are importing into the country where you live and pay tax at customs on import. It is kinda logical you dont pay VAT as a visitor since you dont live there and wouldnt benefit from the taxes you paid. Going further, I remember tax exempt cards in the 80’s you could use and show your id in stores and not pay VAT. Online versions of this exist today, I buy something from the UK and ship it to EU, I can request they not charge VAT as Im going to pay it on import.