And the problem with that is...?
There would be no money for the primaries.
IL is considered a primary state, but at the township level it is optional. The state sets a date and each party in each township can either run a primary or hold a caucus. The purpose is to nominate a slate of township officers. Parties hold caucuses because its a lot cheaper.
In my township, every four years each party holds its caucus. The township GOP rents the local VFW for one evening and volunteers from the precinct committeemen check the registration lists according to state law. There's always a lawyer and parlimentarian kept around in case of questions. All in all it's smooth and inexpensive.