Great Post!
I see your point that governments aren't good at building businesses and turning profits. But blockchain is not only about profits. So I think it is possible for governments to create blockchain based currencies. And I believe the only chance for governments to still maintain a currency is to either create a cryptocurrency or create a digital currency which has most of the benefits cryptocurrencies have (instant worldwide transactions, low transaction fees, etc.)
And if they are instantly accepted by every business and you can pay taxes, fees and government services with that currency, then I think it will have instant mass adoption. But as a side effect it will give legitimacy to all other cryptocurrencies. So that would be good for the world but bad for the government. We will see what happens in India, and China, who is rumored to be working on a cryptocurrency.