If the government will make bitcoin as a form of legal tender, they will absolutely create a division that will mine those bitcoin. A government owned currency should have backed by several coins in order to balance the circulation just like what they are doing in the fiat. But I think that is the main problem why government coundn't recognize bitcoin as a form of legal tender. because they have no control over it, the inflation could happened in that case. Or the hyper price of each coin could be attained which will make new people getting hard to grasp in the crypto world.