No, this is the whole problem. If the total sales volume to the buyer's country is under a certain limit the above holds true. When you reach the sales limit for that country, the seller is responsible for applying that country's VAT instead, and annually clear VAT with the respective tax office.

As you can imagine, keeping track of all these things can quickly become tricky. Not business ending tricky but hard enough to become a problem. A consumer should be presented with prices including tax to avoid surprises, but now prices have to be adjusted at the order stage.