I think you confuse billing with payment processing, those are two different things. Also there are tons of companies that do e.g. use SEPA direct debit to char

I think you confuse billing with payment processing, those are two different things. Also there are tons of companies that do e.g. use SEPA direct debit to charge customers (of course relying on a bank to do the transactions), that's illegal now? I think the legislation concerns payment processing services like PayPal and in general any service that processes payments for third parties.