> It only seems to introduce unnecessary costs, such as mining
Who says you need mining? There's different ways to achieve blockchain consensus, such as proof of stake or proof of existence, you don't need proof of work like Bitcoin uses. Since with a private banking settlement blockchain you know in advance who the players are (individually-invited banks) you can give them a percentage of the network and have each node verify the transactions across the network. You could even give nodes to regulators or consumer advocacy groups to achieve regulatory compliance or consumer oversight if required.
As for cost, you could technically run a PoS node with a raspberry pi, a large USB drive, a wifi connection, powered by a solar panel and an old car battery on the roof of a building. Proof of stake only needs minimal computing power and a persistent internet connection.
Seriously, a lot of the scorn heaped on blockchain technology is unwarranted. Yes, there's loads of hype and bullshit (we're going to get rid of nation states and fiat currency!!!1!), but no more than the internet in 1994 or during the dotcom boom. Yes, lots of crap ideas, but some gems too. It's too early to see what real impact it will have. Criticising current blockchain technology is like criticising early broadband or smartphones.