No banks doesn't deal with bitcoin because bitcoin is still not considered as legal money in our country so till now no banks accept bitcoin. but banks are making themself ready for future with such own currency.
The banks are making ready but they are not taking bitcoin into their system but they are only focused on the blockchain technology since they are also planning to create a digital currency of their own which is centralized. But I believe that if bitcoin will be widely adopted the banks have no choice but to create a scheme wherein bitcoins is included.
Directly? In our country we have that and we have an application or bitcoin wallet that is exclusive only in our country and you can cash out your bitcoin directly to your bank or ATM machine because it is supported in that application. although it have a small fee but the function of that application is hassle free because that is instant so many of my country men use that application too. You can pay your bills also there and buy game credits. That is in our country but you can search if you have a application in your country just like us.
Your country sounds like an ideal place for bitcoin users to live so I'm just curious which country you mentioned 
Anyways, I still see that bitcoin is not fully accepted and used in banks, banks are just for cashing out bitcoin, is that right? But it's way better than where I come from, banks here don't even like the idea of bitcoin, so there is no hope of cashing out money from bitcoin through any application.