Internal transactions all over the world are routed through US companies. I have paid using Visa or Mastercard at some point in Australia, Indonesia, India, Frnce, Sri Lanka, Singapore, Dubai.....
its not exclusive, but there is a problem with network effects. From the point of view of a business why should they add support for a new payment system no one users, from the point of view of consumers why should they sign up to a new system that no one accepts?
As I said in another comment the most likely alternative is a more decentralised system that all countries/currency blocks that want sovereign payments can get behind.
It's a problem for two reasons. First of all it means American companies get access to a lot of privileged information. Secondly, them pushing foreign morals eg sexual content or services being blocked.
If there were an EU card system id certainly sign up for it and demand from vendors that they support it. I don't want my data ending up in America especially these days.
The network effect will work out fine because we have reasons to want it.
Its a problem but a global one, not merely a European one.
Network effects are very powerful.
You might care enough about privacy but most people have given up.