They already did. From my memory, there is several major banks, including Central European Bank, which clearly said to people that it was dangerous to invest in Bitcoin, and that they should focus on their investment plans with ridiculously low yields.
There is a distinction to be made between central banks and commercial banks, isn't there? Commercial banks will provide financial services if there's demand and as long as they are government-sanctioned. For now, it looks like bitcoin is being sanctioned and regulated.
Central banks feel threatened because people are increasingly looking for good investment opportunities and places to store value -- outside of fiat currencies and a bubbling stock market. But I don't know what a "war" would look like, because it seems like governments are mostly approaching it favorably at this point.