That is a possible way but I don't think that this is enough. They can introduce their own wallet but they cannot force their citizen in using them, unless they will create a law for it. The users can easily create wallets from their smartphone, laptop, desktop. Also, I don't think that the citizen will use that wallet because the government can easily block their wallet, security issues, hacks, trust issues or whatever reasons. For me, it is a good approach for the government in order to govern bitcoin but I don't know if it will be effective enough.
A law regarding cryptocurrency wallet will serve as an announcement to people that such thing exists. Unless almost everyone already knows about cryptocurrencies, this announcement will never happen. Ask yourself, is there anything that's mandatory that we should have? Is there a fiat wallet that we're supposed to have? We don't. But we're supposed to earn fiat in order to survive.
Right from the start, we're all programmed to earn fiat. We all went to school so someday we will get out of poverty using that magical currency that we're all looking for.
If the government would want to control us by making us all use bitcoin. Then they will do the same thing that they did with the fiat currency. It's required to have the coin, and there would be given wallets for different jurisdictions. But since the nature of bitcoin is all about anonymity, I doubt that this will ever work out.