because you don't always want to "control your money yourself".
You may want to have some services easily available.
Maybe if that "bank" will use a multiSig wallet, it would be possible to create a sort of bank but only with a multiSig function. However I don't think that now a bank is a primary important we need other service (like pay in fiat -> btc , pay the bills with bitcoin directly, etc...)
You can pay with bitcoin directly if the company that is issuying the bill is accepting bitcoins.