Banking system doesn't need bitcoin any more than it needs cancer. The banks handle fiat, why in the world would they support something that's openly anti-bank & anti-fiat?
For the same reason news papers supported their websites despite that their websites are openly anti-paper!
For the same reason telecoms supported Internet despite that Internet is openly anti-telephone!
Those businesses don't need Internet any more than they need cancer but... they have to adapt or die!