Visa/MC cozied up to major national banks in different countries (not just in the EU) and offered them a sweet deal the banks could not resist: ditch the national payment network in favour of our own cards and we will give a slice of each transaction fee. The transaction fees are tiered, with one part of it going to the payment network (Visa/MC) and the bank (card issuer) keeping the other part. For cross-border transactions, there is also (of course) the exchange rate that comes into play, and this is where each bank buffs its transaction profit margin up even further (as each bank sets its own exchange rate rather than using the interbank exchange rate), so…
… banks saw big, no, BIG $$$ and lost their minds. The transition was rather swift: between the very late 2000's and approximately 2015 (give or take a few years), the transition had been complete. Credit cards became a massively profitable and booming business for the banks, with all sorts of loyalty programmes and bonuses (at consumers’ expense, of course, as the banks also jacked up interest rates on revolving credits). Note that all of this took place before national governments stepped in to regulate the transaction fees.
This coincided with the growing allergy of Western governments to owning any critical infrastructure (including payment networks) and the rising trend of outsourcing as much as possible to the private sector. As it is easy to imagine, it did not take long for the national banks already being in bed with Visa/MC to convince their respective national governments to stop investments in maintenance and enhancement of domestic payment networks and delegate the payment processing to the cartel: «they can do it better than you do».
… all of which has led us to where we are right now. Technically, national payments are still alive, but they are more in the contained mode of operation and not in active use or development.