Pretty much all banks use mainframes to do batch processing. "SFTP runs the world".
I got heavy into fintech a couple years ago, and at first I thought "This is all insane." I was coming from a SaaS world where it's easy to think about transactional guarantees with API calls.
I finally "got it" when I realized that pretty much all of our financial system in the US is based on the digitization of manual processes from the 50s and 60s. If you think of how banks worked before computers (e.g. large binders of ledgers that were manually reconciled), that's basically how it still works today, those big binders have just been turned into digital files that are processed by machines.
I'm no fan of crypto, but the one place where I can see real utility for blockchain is as a backend settlement service for banks.