RSA alone isn't enough. How do you use RSA to build this? You can do auditable sums (prove that private balances sum to a public total), but I can't think of a way to do things like proving that a particular debit happened.
> costs virtually nothing to fix.
There is very high system-wide cost to the status quo. Part of the reason that bank errors are so inexpensive to fix is because transfers take 2-5 days.
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.
Credit cards basically do this. Part of the reason they are able to is because they gather more data and rely on more sophisticated technology than the banking system. With blockchains, you have another small tool to improve the situation.