And several European countries had their own card systems. The banks have just decided that letting US companies do the work is more lucrative. It was definitely cheaper and it was necessary if they want to be part of US hegemony network and trade with Asian countries since many of them had bad relationships due to colonialism.
The local card systems still exist in most places, but they only work if you have a card from that country, for people travelling across Europe its useless as once you cross the border people won't accept that card anymore and you're back to taking only visa/mastercard.
Eurocheque existed for a long while for Europe: https://en.wikipedia.org/wiki/Eurocheque . But yes, trusting the US economic and political partnership and also choosing the cheaper option, the European banks eventually decided to not do the legwork of establishing a (global) payment network and settled on American Visa and Mastercard networks.
