I do believe that they don't fear cryptocurrencies, losing their customers rather. The fact that they were trusted by people with their money to be exchanged in a typical currency (the one that we usuually have in our country), would be affected if people would go and put their money in to invest in cryptocurrencies, and this currencies will be using digital wallets instead of bank accounts. Also, they don't recommend people to invest becaue of it's volatility.
Cryptocurrency must to has the government support it to help it become popular more on the world. Without the government, cryptocurreny can not approach to everyone and a lot of people will do not know what is cryptocurrency and how to use this currency. Therefore, for me, the banks does not fear cryptocurrency at least in next 20 years up to a century.