Good point. Because of crypto's inability to become an independent medium of exchange, we'll always have the need to interact with Fiat somehow. Banks are known to be the gateway from crypto land into the Fiat world. Without them, one cannot exchange cryptocurrencies into Fiat as there's no central issuer. On the other hand, one cannot live without crypto as it provides freedom to our financial life.
As such, everything in the world needs balance. There cannot be a single thing for any purpose in life. Which means, that diversity is needed for our world to change for the better. Banks and crypto will turn their separate ways for the foreseeable future. But they cannot destroy each other in any way.
The main reason Banks have been against crypto is because they don't want people to gain control of their financial life. Banks' living is based off fees from its customers, and if that's gone, their business will end for sure. While Banks are against crypto most of the times, they're not against Blockchain technology which powers most (if not all) cryptocurrencies known today.
Banks have seen Blockchain as extremely beneficial to them, that they have started exploring the technology more thoroughly. Before you know it, a new age will come where Fiat will no longer exist physically, but it will live on a Blockchain of its own. All in all, both ends (Banks and crypto) will survive for a long time. Just my thoughts