No. i dont think any bank accepts bitcoin because bitcoin is not controlled by the government and all the banks are being controlled`so i think that those 2 won't ever combine because bitcoin is a unstable coin aswell.
No few banks is accepting bitcoins, as you said it is controlled by governments and they have not permitted the use of bitcoin, once they permit can use the bitcoin.
Maybe if the bitcoin is can be used and can be legal in many country. And i think if bitcoin accept in bank, our government will controlled it. And if that happen government always likes to put itself in the center of things, so they just can't stand the fact that they are issuing laws, and people might obey them.