The banking system will exist almost as long as the state exists. After all, the banking system serves the economy of any state and is actually part of it.
Bitcoin or cryptocurrency is generally not capable of destroying the banking system either in theory or in practice. A decentralized cryptocurrency should not conflict with the banking system, otherwise it may lose this confrontation. A decentralized cryptocurrency can and should develop in parallel with the current payment systems.
Banking system serves as the main financial institutions of one nation, it represent the strength of the country. There's no need to compete if there's a chance to use the same system such as blockchain. Both currencies will be able to co-exist without any problem if they will allow both sides to transact and adopt both system. it will be difficult for BTC to break the financial institute so there's no need to try doing it, but instead embrace things as part of its existence and future success.
This is not necessarily true that it only represents the strength of a nation as you call it. Banks are well known to be functioning as rent-seeking institutions that slow down innovation tremendously and hinder change on purpose. Their business is the easiest you can have in the world. You just take a straw and out it in the streams of financial transactions, and then you start sipping step by step. For every single transaction that goes through your system you just take a sip. Sounds good? Doesn't really sound like a good system to me.