These bank could have on their own accord taking advantage of crypto in this process that you have elucidated which can be of profit for them too with all the processing fees charges that will go along with. But the problem they face or are facing is that they are under the control of the Central Bank of the country they are operating, until the country's central bank gives a go ahead for banks that are willing to involve in the crypto market to get in, none of these commercial banks will want to go against the Central Bank policies that regulate their operations and scope.
Even in nations that give greenlight for banks to do this, they are still not doing it. Plus, we need to remember that almost all of the banks are under holding, which means that X company owns Bank, and that means X company could own multiple companies, a company that is a bank, a company that is an energy one, a company that is a bakery if they want to. So that means, same company could own an exchange as well, making it easy and seamless for transfer of money between the bank and the exchange, hence would be in. But in no case, they are getting in.
Because security is irreversible. In banking industry, if I steal money from you, then they can reverse it, and justice can do something about it, but if I steal your crypto, you can't do anything. Same goes for banks, no need to take that risk for them.