You can use a smart contract to eliminate the trust in the intermediary bank, so eliminating that counter party risk
bankC creates a secret number, hashes it and sends it to bankA. bankA sends money to bankB locked to hash. bankB can't get money until they have that secret number. bankB sends money to bankC locked to hash. bankC reveals secret number to bankB to unlock that money. bankB does the same with bankA.
Tada, we eliminated the risk of bankB running away with money. This is the lightning network
Cast your mind back to 2008 and hopefully this means that one bank falling over doesn't bring down the whole system.
This isn't a real risk with correspondent banks. Instead, it's counterparty risk: bankB failing while it holds the funds in transfer. That risk can be mitigated with smart contracts, but it's not eliminated. (Correspondent banks also take a portion of the client bank's fraud and AML risk.)
Bank failing in this context would be the bridge (EDIT: contract) gets hacked. Hence mitigated, but not eliminated.
Correct, but in its place is a new systemic risk with a real-world nonzero probability: the contract itself getting hacked. There isn't analogy for this in modern banking since the equivalent issue would either (a) get rolled back or (b) fold into the bank failing envelope. (There is analogy in pre-modern banking, though it largely revolved around debasement and invasion.)
The goal of the transaction is for the Spanish bank to have access to USD. In the example given, the Spanish bank would then have to take the crypto it got and trust an exchange to give it USD in exchange for the crypto.
How do you get USD to the Spanish bank without trusting a third party?
Maybe the Fed themselves will issue tokens in this way. It's also entirely possible to construct a permissioned, yet decentralized exchange of tokens among whitelisted parties.
Either way USD is never sent trustlessly.
The sender and receiver still benefit from a permissionless, automated, international, instant transfer of funds with a cryptographically certified audit trail. The blockchain runs 24/7 and has no downtime. A token can be fully programmed and fine tuned for whatever parameters need to be checked to authorize a transfer. Those rules are transparent and auditable to everyone involved.
The transfer goes through within seconds and the cost of the transfer does not scale with the value of the transfer.