If they could get away with saying that Bitcoin eats babies and will likely result in the flipping of the earth's magnetic poles they would try that excuse instead.
Unfortunately for them, that would make them look silly so instead they latch onto the next closest thing that they can, which is the AML / KYC provision that financial institutions know their customer (as in how does the customer earn money, are these funds deposited by the customer earned in a legal manner, etc.)
Ok, now that is a different question. That one is simple. Banks have a hard time dealing with fraud. They don't require that their customers all use two-factor authentication. Hell, most of them let you reset your password through the e-mail, and they consider it secure because some even insist that you you know your dog's name (yes, the same name you just Tweeted about or commented on in your publicly available Facebook page.)
So rather than deal with the risk that fraudulent transfers will be routed through accounts of bitcoin exchanges, they would rather keep their heads stuck in the sand. (Well, that isn't entirely true. See most bank executives are just two more annual bonuses away from retiring, and if this whole bitcoin thing can just be put off for a while longer, the costs of imposing proper security won't be incurred until after those bonuses have been paid. And since neither you nor I are allowed to open a bank to compete against them, they can continue to get away with the crap that they do, like not serving customers that are unprofitable.)