The only payment method that works with recurring and more or less "final/instant" transactions is credit card.
So there is no alternative for SaaS or in-app-payments to credit cards (or some direct debit risk mitigation business like paypal)
This sounds highly doubtful. Care to explain?
There is no validation except some nummerical tests. You can enter the number of some charity or your landlord when doing an order at e.g. Amazon.
To deal with that risk, every bank account holder has the right to chargeback transactions without giving a reason. That's why banks typically keep a lot of the money you invoice for a grace period of approx 6-8 weeks. And companies like Otto have their own credit check companies…
tl;dr if you instantly deliver items or services, direct debit is not safe.
That is... simply not true. Or perhaps I am misunderstanding what you are saying. There isn't a bank in the EU that will allow you to make a transfer from an account that's not yours (authenticated by whatever means - card readers, digipass, RSA keychain gadgets that display a new number sequence every minute, etc.).
Safe payment methods are advance payment (since there's no reason to allow someone to charge back an order they've explicitely placed at their bank) and cash on delivery (though that's expensive). Which is why some large merchants (eg. Neckermann) restrict payment options to these two for the first transaction.