Your argument is mostly invalid as H&M, for example, has tags in multiple currencies. And as a non-Euro Romanian I can tell you that the conversion rate is not favorable to the buyer.
It true that they don't do it for most of their products, but that doesn't change the fact I have seen such price tags.
The initial argument would only be valid if prices in different currencies would be smaller in the poorer countries, which doesn't happen anyway, regardless of currency.
But it does happen, on average H&M products are cheaper in Portugal than on Germany, except for those few cases I happened to stumble on.