I don't think that banks have any particular incentive to accelerate the adoption of Bitcoin, but history demonstrates that they do eventually change when the stress is sufficiently high. Consider how the internet began, how it was disregarded by traditional institutions that then opposed it, and now they cannot live without it. There are already some smaller banks who are testing custody services due to client demands, despite their late mover status by the big banks.
 The moral of the storey here is not that banks should legitimise Bitcoin, go ahead and use it as it was meant to be, peer to peer, and continue to use it until such time as they do.