I'm legitimately curious how these American payment companies held onto their worldwide dominance for so long. I'm used to seeing the sign at restaurants of all the other cards they accept, but for so long I've only ever seen Amex, Discover, Visa, and Mastercard in folks' hands.
Bank deals, especially in Europe where debit cards is more popular than credit the issuing banks preferred deals largely dictate what network you'll be on.
Its simple: they have deals with all the big banks who issue the popular cards with all of the rewards, so those are the cards people get.
geopolitics, dollar, and then network effect. in that order.
Amex is not very popular in Europe. Discover... I am not sure, not that much.
Visa and MasterCard are everywhere though
There is a huge first movers advantage on infrastructure.
Additionally until recently most political parties and people in the EU didn't see this as national security related infrastructure. That's why it was allowed to be privatized and handled by external companies. There is a lot more critical digital infrastructure that is being moved away from. Think Microsoft office suite, operating systems, cloud systems and more.