I am not an expert on this topic but... The central banks of eurozone countries are governed directly by the European central bank. They are not controlled by each member state's government. Eurozone also means they all use a single currency and are all members of the single European market. There are no different laws for cross border payments.
So I guess there must be another reason we don't know about.
No expert either, but there is definitely domestic regulations in place. Besides, the eurozone is only a subset of EU. The UK has its own currency, for example.
So I guess there must be another reason we don't know about.