If we were to go to a 100% bitcoin currency system. The banks and governments would loose control of whole financial system. The present governments would loose control.
Thing is that you are constructing this thought on the basis that fiat existed and banks controlled them and then bitcoin came in. But this is unrealistic however optimistic we become. Bitcoin being the only mode of transacting would take a long time for the people to accept and use.
Then again banks are way more clever than us. They know how the tables can be turned and they may end up being pro-bitcoin with the actual thought of being the big whales of bitcoin. Nobody knows what will happen in future but bitcoin will be a cult system for now.