The cost is here due to AML regulation. If government wants to outsource its duties (crime intercepting) to banks, then perhaps it should be government to pay for it (in the similar manner it pays telecoms for wiretapping).
I fully agree that the cost of the AML/CTF should be on the government.
However a bank still needs to work out if they will risk accept customers.
For example my CRO presented to me the cost of enhanced due diligence for Delaware companies. It was cost prohibitive so I argued that we should not bank customers who are too complex for the next 12 months.