Is it possible that banks would accept bitcoin as your deposits directly from your bitcoin wallet? Or they will ban it because of internet security reasons?
No, it's impossible they the bank only interested in the technology behind Bitcoin, the blockchain. The reason why do banks hates Bitcoin is because of Bitcoin's nature decentralized, What's the exact reason they should adopt Bitcoin? nothing. Instead of adopting it they might adopt blockchain in order to transform their traditional system into a modern one. Basically, it against the purpose of the Bitcoin since if you're holding your Bitcoin you have your own bank and you don't have to trust someone to hold your money, you have ultimate control over your money.