This will not happen for several reasons. First of all, people can not live using only cryptocurrency. This requires special living conditions, but they are far from being the same everywhere. In addition, many groups of people simply categorically will not use cryptocurrency and there can be a lot of reasons for this.
The second, and even more spring, reason is that a transition from a conventional currency to a cryptocurrency is necessary for a state, but no state will ever give up its national money, because the normal functioning of the economy of each state depends on them.
That's what I've thought in the first place. However, considering how crypto has become extremely popular these days, anything is possible. What's needed is regulation and mainstream adoption, for crypto to become an independent medium of exchange just like Fiat. Of course, Banks won't be going anywhere simply because they're backed by the government (whereas crypto is not). On the other hand, crypto is largely unstable and unscalable right now.
With all the well-known issues of crypto, living only on it would be just a mere dream. Still though, there's room for growth and improvement within the space. If crypto succeeds, then people will start living off it instead of Banks. Which in effect, would create a completely decentralized economy that's free from corruption or fraud.
Nonetheless, it's good to make a balance between Banks and crypto, as they have their pros/cons from one another. Just my opinion