>I can't think of a way to do things like proving that a particular debit happened.

Prove to whom? Banks have multiple layers of redundancy (including internal logs, paper/PDF statements, etc). So in case of any software error or a single-employee malice, it will be just fine.

>Part of the reason that bank errors are so inexpensive to fix is because transfers take 2-5 days.

That's a feature, not a bug. It gives you time to stop a transaction initiated by someone who stole your identity. With blockchain, you lose keys - you lose coins.