Banks are concerned that crypto could be used for illegal activities such as money laundering and terrorist financing.
This is false, it's not that easy to use crypto for illegal activity, do you think fiat can't be used for illegal activity? go search in google. Even you use a privacy coin, you still need to trust someone and it's sometime will expose your identity, receiving money through bank will make the sender know your real name.
Banks can use crypto to improve efficiency and reduce costs.
Yes. But since Bitcoin is decentralized, it shouldn't be associated with banks or any other third party intermediary.