I think that such a future is possible and quite soon. Deposits in bitcoins will be profitable enough for the banking sector as soon as they legalize the cryptocurrency in many countries.
for this, commercial banks need more legislative initiatives to change their activities which are defined by the central(federal) banks,So I think it means that they don't have the right to do this and to offer bitcoin deposits,For example I know countries where banks create new,independent service/Site which offers bitcoin related services and exchange services,but what you said is not bank's profile and their job is very different, Also it partly depends on how does concrete government see the legal definition of bitcoin.