I am not sure where the disconnect is. Having a database that can provide a permanent unalterable record of all transactions, even when running over a distributed network, seems reasonably important to me.

Are you saying it’s just as good to do this in the application layer? I respect that’s a possible option. Not sure I agree it’s a good option.

That's exactly what I'm getting at. You'll want one layer in charge of ensuring consistency and authentication of incoming write requests.

This can be, but definitely doesn't have to be, a typical relational database in conjunction with a core banking system.