Richard Thompson Ford explains why Michigan - and any other state - can legally take over cities if they feel it is necessary (my 2301s should be familiar with this argument):
.....how local government is organized is up to state law, and the remedy to amend these state laws is the political process. As William Rehnquist wrote in the 1978 case Holt Civic Club v. Tuscaloosa, which upheld Alabama's decision to give cities extraterritorial jurisdiction over nearby settlements, the "authority to make those judgments resides in the state legislature." Citizens who dislike the existing arrangement, he wrote, "are free to urge their proposals to that body."As far as the Constitution is concerned, a state could dissolve all of its local governments and run everything from the state capital. Whether there is local democracy at all is entirely a matter of state law.
Remember that cities and local government are not mentioned in the constitution.