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.
Sadly, up to now, there are still many cryptocurrency investors with that distorted mindset. Those are just silly, ridiculous claims that the government has spread to keep people away from bitcoin, and most people realize that. But why hasn't the OP realized that yet?
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.
What he's saying in general is cryptocurrencies including altcoins, not just bitcoin. And we can also see altcoins like LINK or XRP collaborating and being used in the banking system. That would create a huge effect, but unfortunately it is still a centralized system and they cannot compare to the decentralization of the bitcoin network.