[riskable]

> You can use non-blockchain cryptography to guarantee that.

Not in the same way though. An attacker could still modify the transaction after-the-fact at both endpoints during or after reconciliation processes (sadly, most banking transactions still happen in batch and there's multiple reconciliation processes every day). They could hack the reconciliation process(es) to undo or modify transactions later in the same day or--depending on the banks in question--days later.

Then there's also the possibility of just changing balances at one end of the transaction (flat out) with no way for the 3rd party to perform the equivalent of double-entry accounting to verify that the amount received matches what was sent. Bank transfer reconciliation catches problems like this all the time and it's baffling to me (but apparently has legitimate causes).

A blockchain would completely negate any such attacks and make reconciliation pointless.