Every state will have a different distribution of public colleges depending on history, geography, and politics.
OH has 3 metro areas and several other smaller distinct urban centers.
IL has one giant metro area and the smaller distinct urban centers.
OH was also settled earlier. It’s state and local governments also took over a bunch of privates throughout its history. That never happened (or had to) in IL. Because of that, OH has a ton of publics (as well as a ton of privates).
So yes, 8 of the 12 cities in IL with the most population don’t have publics within it’s city limits. But 7 of those 12 are in Chicagoland. Of the other 5, Springfield, Champaign, and Bloomington all have one. Rockford has one nearby in Dekalb, and only Peoria has to rely on its private.
By comparison, AZ (another state with one big metro) only has 2 publics among it’s 12 largest cities. Granted, ASU is spread over 3 cities, but 8 of the 12 most populous cities in AZ also don’t have publics.