For example in Denmark: "Due to the higher fees charged by banks for the use of non-Danish issued cards (that consist of foreign card network interchange fees plus Danish banks own fees), many Danish merchants only accept Dankort and Danish-issued credit cards, but not foreign cards." (https://en.wikipedia.org/wiki/Dankort)
I really hope that the EU adds some regulation that forces merchants to accept debit/card cards from other EU member states on an equal basis. Especially in combination with the fact that in some cases only electronic payments are accepted, which makes it pretty much impossible for anyone to pay without a national bank account.
The EU already solved (or at least mitigated) the issues with roaming in mobile networks. Doing the same for payments is the next logical step.