Nooo..
If there would be a bank then there will be taxes also.. and there will be someone who knows aboit your account and activities.. wallets are better then banks.
Bitcoin can already be taxed when you submit your yearly tax reports to your local IRS. So in that aspect there is no difference with how the situation is right now.
Another thing is that if a service pops up calling itself a Bitcoin Bank, that it won't be anything like you see with regular fiat banks.
It will just be an existing or a new online wallet service or Bitcoin exchange offering bank like features to people being interested in it.
Most people like the idea of having the possibility of earning interest over their coins, which is also the main reason as to why they would support such an initiative.