The odds are good that these governments will make their own coin. Just take a look at whats happening between US and China. The trade war seems to have them competing on edge and now China has announced that they will be pursuing cryptocurrencies more it seems that the US won't let itself get beaten and is also investing time and resources to look into more blockchain projects and solutions.
We don't need more coins, we need legit coins that are used in the real world. Hopefully these governments can provide these, and that they are exchangeable with Bitcoin and other cryptocurrencies.
When the government begin to create their own cryptocurrencies then the adoption of those coins will be high because they would be a legal way to transfer wealth from one individual to the other, but make no mistake those coins are not going to be any different than fiat and if anything they are going to be way worse, it will be a way for the government to try to keep control of the money supply, so whatever money that you have in your wallet will never be truly yours.
Why do you think that China is interested in creating their own cryptocurrency when they have shown time and time again that they are against freedom? Because in their hands cryptocurrencies will be a way to keep an even greater control of their population.