The bottom line for any of this is that you can't do true irreversibility without fairly strict decentralization; eg, where lots of lots of people/entities can be validators in the system. Bitcoin's miners provide this function, and critically, they do not have to be authorized by anyone or pre-approved in any way. They can be anonymous, join and leave the network at any time, etc. This is possible because of Bitcoin's *economic* incentive structure; eg, earning a token that's *native* to the ledger: bitcoins. Once you remove the native token incentivization, you've necessarily created a system that has to use some sort of pre-authorization; eg, "trusted entities". And once you have that, well, you're back to the problem that the entire idea of a validated cryptographically linked chain of blocks was invented solve in the first place!
These permissioned ledger systems can certainly be a useful tool for collections of organizations, but make no mistake: they fundamentally do not and cannot solve the same problem Bitcoin solves.
Yeah...but to an unimaginative bank, a "solution" is often a trade-off. If all they're only interested in preventing embezzlement, the trade-off thinking would go like this: "Is the blockchain solution
decentralized enough to make embezzlement [practically] impossible? Is it
centralized enough to keep it under control [eg., for rolling back unauthorized transactions]?"
Banks are legacy institutions. They roll with what they got, and their "solutions" tend to be improvements at the margin.
