Somehow they can do that, if the trend became the essential in the future like todays fiat money maybe they will create a crypto that will be the flag bearer of a particular county in crypto world and I guess bitcoin will be the international monetary for cryptocurrency still.
They have the power to do that but they won't gamble their business to something decentralized by adopting a coin that they don't have the authority to control it.
They can create their own cryptocurrency but it can be a stable coin which is not volatile for the sake of their business and customers. It will be a digital currency if they do that but there's no need for them to do it, they have online banking and adoption of blockchain is what they only need to do.
I think banks are aware of crypto currency, it is possible that they can develop some coins of their own, but being in control of it is hard for them, because that is not the way of how crypto work, the price in the markets are so volatile, it may change the value of every coin at anytime of the day, It will be a huge risk for the banks to invest in crypto currency.