VAT is to move the tax burden to the end-consumer in a transparent manner. All companies in the chain reclaim VAT so they do not pay.
As a result, as long as you allow VAT to be claimed in the country of Eu where the sale is done and not the country of residence of the end-consumer it is trivial to shift "perceived business activity" to the lowest tax jurisdiction. It costs almost nothing to add one more company so that business happens elsewhere.
This is different from turnover tax which is paid at every step and not reclaimed. It works in the opposite direction by creating vertical monopolistic conglomerates which control the path of goods from ore to the product.
Neither will do anything as far as digital goods are concerned. The only way to deal with those is to move taxation to country of residence of the end-consumer and that is nearly impossible to achieve.