The value that credits cards provide isn't the network, it's the insurance (chargebacks). And while I appreciate payment insurance when I'm paying for an expensive object from halfway around the world, it's unnecessary overhead when I'm buying a bagel in a cafe.
Visa can certainly remain profitable even with the fee caps but I find it hard to imagine that they would try to enter the EU market if they had no presence in it and there were already several established competitors there these days.
For two decade before that and since then, all carte bleue are visa and vice versa.
Mastercard exists here as a premium level card giving you tons of bonus, and usually fee with your account. Eg my bank account online is free and almost no fee for anything (I pay 9e for extra phone and wallet insurance and next day replacement), and as long as I keep more than 24k in the various accounts and give me a Gold+ visa card and a mastercard with 1% cashback.
Are/were there any in Europe to begin with?
Eurocard made a deal with Mastercard in the 60s which made it impossible for them to enter the US market.
Barclaycard, was as the name implies limited to a single bank.
The were a few other systems that were mostly national and didn’t even expand into other European countries.
Sure there is. Someone had to build the all the software that deals with those encrypted bits. Someone had to scale it up to handling tens (hundreds?) of billions of transactions per year, each one approved or declined within a few seconds.
If you think it costs zero dollars and we can just say "the internet is our payments system" and call it a day... well, I don't know what to tell you. Your expectations are so far from reality that I'm not sure we're going to have a productive discussion.
If you can somehow manage draw this conclusion after reading my comment, then I'm not sure we're going to have a productive discussion.