This is slightly off-track, but germane to this discussion.
I've always thought Cook County should be split into three parts. One would be the city of Chicago, that would have a single unified city-county government, a la Indianapolis and Louisville.
The other two counties would have a dividing line roughly along the Ike. The third largest city in the nation, already with a mayor and 50 aldermen, doesn't need a county government on top of that.