Hell know I wouldn't trust any bank with the one currency they don't have control over. Start letting them loan out your Bitcoin and extort interest rates from the victims/customers then in a very short amount of time they would corner the market as usual.
The above is a disaster for Bitcoin but you would clearly get many people fall straight into their game and hand over their Bitcoin. Tut tut.
It is against the Idea of Bitcoin, but if the bank can give good reasons to trust them, why not give it a try?
You answered your own question lol