This deserves reiterating:

The whole value proposition for the bank having a customer service line is to RESOLVE exceptions.

Yes, perhaps the first-line customer service should stick with the policy. If they cannot handle the situation (either to lack of knowledge or authority), the first line reps should ALSO FIND and ESCALATE the exceptions to a rep who DOES have the knowledge and authority to resolve the problem

When a company does not do that, they demonstrate that, despite all their marketing statements that they care about and value their customers, they, in fact NEITHER give a fck about nor value their customers.