Comment by rkomorn
It helps that, to be able to use an IBAN for withdrawals, you basically have to "sign" a recurring transfer agreement. Otherwise it's pretty much always a "push" transaction from buyer to seller.
Better than being able to commit ACH fraud merely by virtue of having the bank's routing and account number.
Side note: shout out to both MB Way and Multibanco payments in Portugal that have made it so I haven't have to give payment information to an online vendor in years.
But there is no cryptography or any kind of identity verification involved in "signing" such an agreement. If I know your IBAN I can subscribe to such an agreement on your behalf.
I'm not sure about Europe, but at least in the UK, what makes such a system secure is that the account holder can reverse any "pull" transaction for over a month, with the merchant being on the hook. So it reduces the incentive to exploit it (or at least shifts the risk off the account holder), to a level where it's pretty much never done.