This is one of the problem with banks and we need to be very confident when making transactions with them. The government uses the bank to scrutinize us and get information about us. If all banks start allowing customers to make deposits using Bitcoin, that means there will be no privacy again and everything about us will be leaked to the government.
The way Bitcoin is operating is better for us allowing people to make transactions without their privacy information like name, location to be attached on each addresses. I know the government will do everything possible to get access to us even though transactions through the blockchain can look very hard to track individual users.
Well, that's the plan. To "deanonymize" as much Bitcoin users as possible by forcing them to go through KYC. Governments did this with centralized exchanges, and now they're trying to do it with banks. I think they will succeed. Especially when most people don't care about their privacy, or even decentralization/censorship-resistance. They're only into Bitcoin for the money.
By providing Bitcoin-based deposits, banks can benefit from market price volatility. They'll be able to make more money this way than simply investing in stocks. Pretty smart, huh? I hope that despite these efforts, Bitcoin remains decentralized. The community must stay strong no matter what. We'll see what happens in the long run.