I can't speak to banks, but I have some personal experience with this sort of thing in the case of trading. I'm guessing it's at least somewhat similar to how it works among banks.
All the big players have got real-time feeds they're sharing with each other to keep track of who's made what transactions, and they're constantly reconciling them against each other, to make sure that everyone's looking at the same picture. There are also daily reports summarizing the previous day's activity, and they are also reconciled as a second check. The proactive parties work together to sort out any discrepancies they find as soon as they find them.
None of this is strictly necessary, because there is a central source of truth that you can rely on. But it tends to operate much too slowly for a lot of people's needs, and mistakes do happen, and they can be costly, so it pays to be proactive. Meaning that, in general, nobody's actually relying on the central authority to keep this organized.
The actual real-time feeds are log-structured: You can add new records, but not delete old ones. If you want to reverse a transaction, you just add a new entry to the ledger to back it out.
In that sense, it works a lot like how a blockchain would work. The only difference is, nobody's bothering with all that crypto stuff, because all it would do is make the whole thing more expensive. Like, literally, that's the only impact I can see. It won't help with preventing errors - when mistakes happen, it's invariably because of an error at the boundary of the system, and fiddling around with hashes of the previous message when sending new ones does nothing to guard against that. All it would do is slow both the throughput and latency of transactions by introducing more spots where synchronization must occur together with a bunch of ancillary computational load.
In a world where time is money, that sure sounds to me like a $100 solution to a 1¢ problem.