It's a really interesting question. In Japan there is already a large movement towards shops accepting Bitcoin. Once LN are implemented this will become a cheap method of transaction even for small payments. The next step is for people to start being paid in Bitcoin (which comes as a natural step when shops accept Bitcoin as payment, because they will want to be able to spend the money they are receiving). At which point it's all out of the hands of the central banks.

So what do they do? They will look to break that cycle somewhere. Or issue their own "regulated and safe" version.