I suppose the most problematic would be traveling. I recently when outside the EU and was surprise how smooth the process was using my Visa card, to the point I didn't use any local currency.
On the other hand, I recently buy books from the UK and it get stuck for two weeks in customs, and it had nothing to do with the payment platform. I had not realized how difficult is to import something from outside the EU, even for personal use.
The big benefit is that all internal EU card transactions are no longer routed via US companies which is quite ridiculous.
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.
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.
Network effects are very powerful.
You might care enough about privacy but most people have given up.