I have a similar situation here.
Buying or selling bitcoins, a bank supports me.
Of course they charge a little fee. But for them that is easy earned money, and for me it gives me some kind of security not getting scamed.
The bank and me, we both benefit from bitcoin.
You just explained the reasons why banks don't fight Bitcoin. Because most people just trade Bitcoin for fiat and then cash out. Banks earn money and are happy. Instead if users will start to completely bypass banks and only use Bitcoin, without cashing out in fiat currency, well, I think banks would be much more afraid...