Do you also consider Google and Bing on the same footing?[0] No, right?. But in anycase, fair enough, the technical correct one is duopoly—the problem just is, it doesn't make it any better.
Oligopoly. Discover card and American Express are both mostly accepted (I say mostly because some companies don't accept American Express due to their charge back policies).
And yes, it makes it so much better. True monopolies can slack so hard and yet still rake in boatloads of cash because their customers have no other option. Google cannot sit around on their search engine or other companies will steal all their customers. Just look at how duck duck go is growing in popularity.
And yet here we are, living in a world where PayPal, visa, and MasterCard are successful able to censor lots and lots of people.
So, by definition, this is a problem.
We would no longer have a problem if we get to the point where a single company censorsing your transactions is no big deal because a dozen others will immediately step up in their place.
But we don't live in that world, and so because of this we have to recognize that there is indeed an oligopoly problem.
Does that matter in Europe? From what I have read here, most people use debit cards (interest rates for credit don't matter) and the fees are capped super low so the % fees don't matter.
I'm not entirely sure what your question is? If it matters that Discover and Amex is not being accepted?
Most adults will be using credit cards, unless you haven't proven to your bank yet that you are trustworhty (i.e. just moved to the country). Debit is usually younger people, below 18 (at least in DK). Both are still Visa or MasterCard.
It would still be a problem, if as a merchant got banned by Visa/MasterCard, since now they have no other way than to accept cash, which obviously doesn't work if you are an online shop.
This really depends on the country. In Germany, most day-to-day payments happen with cash or over the Girocard network. I got by for most of my adult life without a credit card. The only thing that's kind of tricky is booking a hotel without one (international hotel chains have standardized their registration systems around credit cards). I only got a credit card last year because it's free with my current checking account.
And yes, it makes it so much better. True monopolies can slack so hard and yet still rake in boatloads of cash because their customers have no other option. Google cannot sit around on their search engine or other companies will steal all their customers. Just look at how duck duck go is growing in popularity.