You can pay using SEPA bank transfer or direct debits or some other options.

That the bank is using VISA/MasterCard etc for their cards is still a better option than using them directly because they barely do anything. Heck European debit cards don't even work like they do in the US. You HAVE to 2FA them.

Most of the time in Europe our transactions go through things like iDeal, Bancontant, Wero etc

Not only that, but even if you manage to find a platform that isn't directly owned by them, they are payment service networks. They are there along the way to facilitate transactions and manage relationships with merchant services. There is no escaping them.

In Italy we have PagoBancomat, but that's a debit card, not a credit card.

If you buy online, you can also use PayPal connected directly to a bank account, no credit card necessary (PayPal is also a shitty company, but sometimes there's no alternative...)

There are some surviving national circuits like PagoBancomat (as the sibling comment from Scrollone) and Dankort (Denmark) and girocard (Germany). My personal impression is that they are slowly going out of fashion in favor of visa/mastercard only (probably because they can't offer better prices than them).

I don't see a solution to the duopoly, apart from lobbying politicians to support this national payment infrastructure. Especially in recent times I can also see how some governments might not want to rely entirely on two US companies for running their entire economy, so something might move on that side, so there's hope on that side.

The EU has already been moving on this front in the last years by forcing the banks to provide programming interfaces to initiate bank payments, and that's why you can now see more and more options to "pay by bank" online in EU. These online payments generally skip card circuits and run over normal SEPA bank transfers.

More info here on the last part: https://en.m.wikipedia.org/wiki/Payment_Services_Directive