In parallel with this trend, European countries are getting increasingly fussy about which cards they will accept.
Recently, railways in The Netherlands, for example, wouldn't accept cards that had Visa or Mastercard logos - only V Pay or Maestro (European debit card variants). These latter aren't even routinely issued in the UK where most debit cards are branded Visa or Mastercard and are viewed as "credit" cards in most European countries. If you wanted to buy a railway ticket in Amsterdam station, your best bet as a visitor was normally to withdraw cash from the ATM and then queue at the ticket counter. There has been a recent change of policy, but you'll pay an additional 50c for the privilege of using your Visa/Mastercard.
You'll also find that stored-value cards for things like transport are increasingly common and often the only way to get the best-value fares. However, the card will likely have limited geographical scope (eg the London Oyster Card), so if you're travelling widely you'll need a bunch of them or pay higher fares.
While these schemes may make life easier/cheaper for locals, they can make life for visitors increasingly complicated.
Mind you, these supposedly transnational card networks have always been rather parochial. A lot of years ago I came across an ATM in Germany with a handwritten signed attached saying "Nur Deutschen Eurokarten"...