The exact count differs by source with the most being 8923 divisions reported by the Chicago Civic Federation and 6042 divisions reported by the Illinois Department of Revenue. See https://www.civicfed.org/iifs/blog/inventory-local-governments-illinois-differences-among-reporting-agencies
This is by far the most of any US State, with both Texas and California having several thousand fewer local divisions, if going by the maximum numbers. Also, Illinois may have the most formal administrative divisions of any subnational jurisdiction in the world though there does not seem to be any compiled list.
Many, if not most, of these divisions must have been approved by the State government at some point in time. So it seems likely there's a rationale for doing so somewhere.