> A) allow for secure payments without giving away something like a bank account # or debit card number
You can use PKI for this. The public key is public and the private key never has to be online. That's how (most?) crypto works, but the system doesn't have to be a cryptocurrency to work like this.
> B) ensure that, even if those payments were secure, there was no other cheating, such as people at a bank just deciding to initiate an account with one million?
You can have public ledgers without crypto, there's usually no reason to do so, and good reasons not to do it (privacy, funnily enough).
Crypto is _a_ solution for this, not _the_ solution, and not even the best solution at that.
You can use PKI for this. The public key is public and the private key never has to be online. That's how (most?) crypto works, but the system doesn't have to be a cryptocurrency to work like this.
> B) ensure that, even if those payments were secure, there was no other cheating, such as people at a bank just deciding to initiate an account with one million?
You can have public ledgers without crypto, there's usually no reason to do so, and good reasons not to do it (privacy, funnily enough).
Crypto is _a_ solution for this, not _the_ solution, and not even the best solution at that.