Government needs to make bitcoin a legitimate legal tender for digital marketing. We are no longer on analog age where everything has to be done with counter banking, we can improve our systems by allowing bitcoin to do most of the human jobs. Buying and selling of stuffs by easily ease stress.
Bitcoin is not some sort of AI that can do human jobs, Bitcoin itself is a currency, and i don't see a way it can help develop the traditional banking system as they both operate in a different way. Having said that, in traditional banking these days everything isn't done over the counter, there is of course mobile/internet banking and a lot of digital stuffs that makes banking quite easy.
Has Bitcoin the potential to replace the banking system? Yes, of course. That's what Bitcoin was invented for.
I'm afraid Bitcoin does not have the potential to replace the traditional banking system, neither was it created by Satoshi for that purpose. Bitcoin was created to be an alternative peer to peer currency that would function/work without any third party, it can definitely co-exist with FIAT and the banking system.