I would say it peaked with the opening of the North Course at Olympia Fields, which I believe occurred in 1925. As of that time, there existed some great iterations of classic golf course architecture: Chicago Golf, Shoreacres, Glenview, Knollwood, Beverly, Olympia Fields, Midlothian and Flossmoor, to name but a few. I'm not as conversant with the merits of some of the courses up north, but North Shore, Exmoor and Old Elm were all in existence at that time as well and I'm sure that there are passionate supporters who would talk them up as well.
In fact, looking at this list, it compels me to lament how few architecturally great golf courses have been built in Chicagoland since 1925. I would only put Conway Farms and Butler on that level. Some might argue Dubsdread belongs in their company, but I think it falls a bit short. I haven't played Black Sheep yet and knowledgeable people say great things, so I'll hold out some hope. To me, the rest are pretenders.