Fiat has lost its value, but we still can't do without fiat. The banking system will always be needed to some point, but their business won't be booming the way it was in the past decades if they don't adapt to trends and what people are interested in. Indeed, they will run out of business pretty soon.
Their policies, charges, low interest on savings, slow transactions, etc., will make all their customers move away from using it. In terms of overprinting local currency, which has ended up devaluing it, that's the decision of the central bank in collaboration with federal inflation won't want anyone to save in their local currency.
As long as governments exist, don't expect banks to go anywhere soon. Besides, Fiat money allows governments to have full control over our financial life. Would you imagine banks disappearing in the future? That means zero control or monetary policy changes by the government. I know crypto (especially Bitcoin) is very popular these days. But I wouldn't count on government ditching Fiat in favor of decentralized, private monies. Not now or in another century.
I'd say banks and governments are only into Bitcoin just to make a lot of money. Not because they believe in it. With the huge taxation benefits provided by BTC, it would be dumb enough to ignore the craze. Banksters, governments, and institutional investors are smart. I'm afraid we aren't, especially when we're letting such entities accumulate a large portion of the circulating supply. The more BTC ending up in their hands, the worse. Ultimately, banks will adapt as they switch to the new digital Fiat system (CBDCs). Expect the erosion of privacy and freedom in the near future. Just my two sats.

You make a very good point. No matter how powerful cryptocurrency is, it is ultimately controlled and regulated by the government, and it will go nowhere if the government bans it. Don't forget, Governments and banks are the ones who control this world. So it is naive to think that cryptocurrency will threaten or make them extinct if they do not adopt it.
No doubt, they accept bitcoin not because they are afraid but because they do not want to miss out on the huge profits and taxes from it. If they really believed in BTC and wanted to adopt it, they wouldn't have created CBDC.
The government is gradually intervening and taking complete control of this market, sooner or later it will become centralized and tightly controlled by them.
Come to think if ever they would be having that full scale ban or prohibition about crypto transactions.
1. Banning make use of banking services
2. Banning on money remittances
3. Banning on those e-wallets or digital banks
It might be that so few bans above but pretty much sure it will definitely be giving out that huge effect on how people would be able to cash out their coins/tokens
that would be converted into fiat. Its not bad to be that positive towards crypto recognition and adoption but it is just that quite delusional or being too much positive when you do already think off that banks would cease to exist or would be extinct or would be eradicated if ever they wont be accepting crypto? Come to think on whose the one first that did exist? They dont need to adopt something because they can stand alone if they wanted to and considering that humanity has been that trusting them since the beginning of time or when these banks had existed.