As a European that moved between countries, I was very surprised when I learned that SEPA allows a "pull" mechanism even exists. I lived 30 years in Latvia without knowing this is a feature in SEPA because every single payment is a "push" mechanism. I'm not sure if banks can turn this feature off, or if it just culturally never gained traction.
On the other hand, payments via banks are fairly widespread C2B, because every bank offers a (custom and horrible) API that merchants can implement. So users can authenticate directly with their bank as if it were PayPal, and authorize a SEPA payment to the merchant's bank account.
In fact, services that care about user identity, will often use these bank APIs to perform authentication with a high degree of confidence about the received user information.
Then I moved to France, and every bank interaction is "pull" based. While friction in Latvia came from authenticating before initiating the "push", in France the friction comes from agreeing to direct debiting, and signing various authorization slips. Sometimes electronically, but sometimes you have to send them by mail before you can start paying for a long-running service by bank (this makes it very undesirable for one-off purchases. In fact it is so cumbersome, that I prefer to pay for many services by credit card every month)
> I doubt the claims of very high fraud rate.
If I provide my account number to a service provider, they can debit it without me explicitly authorizing them (I have to sign an authorization usually, but there's nothing "technically" blocking the counterparty). I suppose that could lead to high fraud rates.