There can be multiple uses for a bank-backed crypto-currency. For example, it will make the conversion of crypto to fiat much easier (first we need to convert the decentralized crypto to the bank crypto, and then the latter to fiat currency). Also, in case the banks support their own versions of crypto-currency, it will become difficult for them to justify the continued hostility towards the decentralized cryptos. Eventually, they may be forced to accept the existence of such currencies.
I think that banks are interested in cryptocurrency technology. It is necessary to solve only a few problems and then this technology can be applied on a planetary scale. I think that in 5-10 years blockchain and cryptocurrencies will be used everywhere!