One year I had an epic week of fraud. My credit card number was stolen by someone involved with a local restaurant, the replacement credit card was stolen from my mailbox, and my rent check was stolen from my landlord's mailbox at a completely different address (and successfully cashed!) There was a 3 day period where the only money I had access to was the cash in my wallet because my credit cards, checking account and savings account were all frozen while their account numbers got switched. All the fraud was covered by my bank though.
SEPA direct debit is the usual setup for places where you'd expect to be able to pay via credit card (regardless of fees), and for e.g. small landlords you just set up a recurring SEPA push transfer (basically like ACH push, but free for normal consumer accounts) to the landlords account.
And for direct debit, you can technically just keep an eye out for unauthorized ones (they need to be shown to your bank 5 days in advance) and tell your bank to stop them before they debit your account. But AFAIK it's the bank(s) that owe you the money, though they can in-turn try to claw it back from whoever debited your account without authorization.
Really, the worst one can do with an IBAN is trolling by spamming transfers to it or signing it up for direct debits (and I'd expect that to cause me at most 1 bank day of no funds, while waiting for my bank to reverse a fraudulent debit). But the impact of the latter is limited (just set up a whitelist with your bank and have them auto-reject the spam), while the former is fairly costly (around 20~30 ct with the accounts that don't do fair-use throttling) and quite risky (harassment and KYC).
I haven’t needed the redundancy since then but it’s comforting to know that I have a multi-month cushion to fight with banks if I need one.
I only carry plastic because I find paying with the phone a bit cumbersome and besides the card doesn't have a battery and fits better in a pocket.
I have multiple spares laying around just in case. Sometimes the cats hide one, so what, the branch office is in 15 minutes walking distance.
Internet access is better and much cheaper too.
Maybe because Russia haven't had monstrous incumbents in either place and as a result the market worked as intended.
The one bank that doesn't have branches, Tinkoff, uses courier delivery.