Distributed databases have existed for decades. It's how large healthcare systems maintain electronic health records for their patients across dozens of hospitals in real time.

How is that useful in a bank ledger?

This isn't true: there are not-distributed blockchains.

The definition of a blockchain is a ledger where every entry is cryptographically signed with a hash of the current entry plus a previous entry. There's no requirement that this be at all distributed. In fact, QLDB uses a non-distributed blockchain as its audit log.

Blockchain are often used in distributed systems because of the verifiability of the records; its a way of providing security of history in a fundamentally insecure environment. But there's no requirement that they be distributed, and they add value in non-distributed environments as well - in any case you want to be able to review a history of changes and know that someone hasn't been cooking the books, for instance.

I'll give a real-world example. One place I worked we had databases that had data constantly streaming in from many different sources. Something that would frequently happen would be some data issue that would break applications; often, this was bad data from sources outside of our control. OPs, who's only priority was to get the applications back up and running, would often track down and directly modify records and fix the data. The issue was that some time later, sometime days later, a customer would call and complain about data being incorrect. By then, it was impossible to figure out what had happened: did we get the wrong data from the source? Did one of the import processes mangle the data? Did someone poke around in the database and change the data? We had no way of telling, and investigations would take many hours, often from several senior people, who would frequently in the end have to shrug and say, "we don't know." There were lots of things that could have improved this, with varying levels of success, but a global audit log would have been the first step. A verifiable audit log would have been better, because often it'd come down to us being convinced the data a third party was giving us was bad, and it became an our word vs. their word since we shared the same client. If we'd had a blockchain layer through which every transaction was recorded, we could have rolled back in time and figure out exactly how a record came to be what it was and been able to prove it to the client.

Blockchains are awesome. People who say otherwise have their heads up their asses, and are unable to differentiate between blockchain the technology, and the sometimes questionable uses they're put to. Iron is used to make guns and bombs; that doesn't make iron bad.