I actually feel that if we look at the technical aspects, Bitcoin has many advantages that could rival banks, such as decentralization which can make it censorship-resistant, global transactions that are very possible to be done without intermediaries, and with a layer-2 system like the lighting network, the use of fees and speed in the transfer process also makes it more efficient, so that's why in my opinion, yes, this is also my analysis of its development if it is widely adopted, it is very possible that Bitcoin will replace the basic function of banks as a store and sender of value, but this is only my argument and analysis
Unfortunately the banking system isn't built to be decentralized. It's an ownership of government which consists of some powerful people that control the arm forces, federal, the state and the local governments. Everything they say and pass a law is the final and any other person that dear to go against it is breaking the law, they also create this law, revise it when they like and enforce them as they like, this is how government operate in all levels but this isn't what Bitcoin is about.
Bitcoin and Banking system has some relationship, but Bitcoin is never control. Bitcoin work with protocols, some predefined rules that has to be followed which are simple, that no one can manipulate or change and it's as simple as that. This is what make Bitcoin special, you don't have to worry about questioning of your money where it comes from and why you have the money, you can't do such things in bank that might even cap the maximum amount that should be in your account otherwise you are going to be flagged and reported.