Problem is that if banks use the same technology and put in to their existing network, they will have much broader acceptace and more trust.
Banks using private centralized blockchain technology to make payments through them much faster would indeed hurt Bitcoin a bit. But having to wait a week for a bank to process a payment isn't the only thing that makes Bitcoin better. Banks updating their businesses to use blockchain doesn't change the fact that your money is still "owned" by the bank/government. A public decentralized blockchain like bitcoin means YOU own your money. It means you can send money and pay for things directly with Bitcoin. Paying for things through the banking system still goes through the banking system even if they use blockchain. There is a lot more to Bitcoin than just a quicker way to send money. Banks can never offer all the other benefits of Bitcoin because those benefits have to do precisely with staying outside of the banking system.