Central banks are usually owned by the country they operate in. If the would start selling shares to the public and try to become a public company, that would be nice. Personally I would definitely invest in a central bank. Their funding comes from the government and their loans to commercial banks are usually backed by the government as well. It's a pretty solid business model with a lot of government guarantees. A great way to make money for the owners.
I would never do it. I do not trust the government, and I am not sure, the money I will invest will be never stolen or frozen. It will be much better to work not on the government, but on ourselves. Cryptocurrencies give us this possibility and freedom.