Can I get a bank account which works like a normal bank- accepts EFTs in dollars, has a debit card which pays in dollars, but where my balance is stored in BTC

Can I get a bank account which works like a normal bank- accepts EFTs in dollars, has a debit card which pays in dollars, but where my balance is stored in BTC and everything is exchanged to/from BTC at the current rate on the fly? With enough of a balance, it seems like I'd be able to weather any fluctuations in the exchange rate and my funds would for the most part appreciate at a much greater rate than the measly interest on a savings account. Does that exist? Would that be a terrible idea?