My central problem is that in current pull based systems (both CC and direct debit), the merchant has access to the information to take money from my account. But that information can leak and someone else can take money from my account.

It's insane that digital systems are less secure than cash based system. If a merchant hands me a paper invoice, they can't just take cash out of my wallet.

The merchant should communicate to me where I need to deposit money, and I should put that into my system. The merchant should have little to no information about me.