Banks work because processes performed by humans that were developed before digital computers were invented, not because technology. They have logs of all transactions and are willing to reconcile them manually and are insured/lawyered against loss when they can't reverse an erroneous transfer. Money can take two business days to move instead of milliseconds, and their customers are mostly fine with this.

Programmers are taught that database transactions exist so that when you move money from one account to another and crash in the middle, no money is ever created or destroyed. Well, cat picture websites might do that, but banks don't. They reconcile logs at end of day.