I'm a Wisconsin resident and UW-Madison grad, so I was only looking at the numbers for Iowa and Wisconsin, but I did the math, and there isn't that much of a difference between Iowa and Wisconsin in the percentage of the population who are undergrads at a public university. 2.5% of Wisconsin residents and 2% of Iowa residents are undergrads at a public university. Wisconsin just has more people.
I think it makes even more sense when you look at the nature of the universities and the states' geography. Iowa chose to have a separate land grant institution. Wisconsin didn't; the University of Wisconsin is the land-grant school. But now you're down a university and those students have to go somewhere, and they do: to the smaller universities.
Plus, Wisconsin is more remote and rugged than Iowa. While it's easy to get around the state now, it probably wasn't 50-100 years ago. So it makes sense that you would put a lot of smaller schools around the state. And those schools were specialized. Most of them (Eau Claire, La Crosse, Whitewater, Superior, River Falls, Oshkosh, Milwaukee, and Stevens Point) were normal schools. Stout was an engineering school. Platteville is the result of a merger between a normal school and engineering school, and Parkside and Green Bay were two-year institutions which grew into four-year institutions.
So it's not like Wisconsin has 12 Iowa States and University of Iowas. It has one combined Iowa State/University of Iowa and 11 UNIs