IL law patterns KS law on a state-specified sign being a legal notice that can result in charges beyond simple trespass. So IL is not the only place. My home state of OK follows your description on simple trespass for failing to leave when told.
As to the overall ISRA material, my problem remains with the treatment of firearms as an onerous civil right that can be restricted at a whim. Years ago, many restaurants posted signage about “reserving the right to refuse service to anyone” and that’s been trumped by the various civil rights acts since 1965.
There was an argument before me between the manager and a customer at my local credit union in Florida. The customer was complaining about a “no firearms on premises” sign. The manager, a known lefty, pointed out she did not want firearms present because someone may misstake them for a robber (it is concealed, not open carry btw) and she pays to have an armed police officer present to protect persons on the property. The guy said so what about the parking lot and what about those places I go to before I come here or where I intend to go when I leave? She looked like deer in the headlights at that one and simply continued that was their policy. I just said nothing and went about my business, armed. I abide by the premise better to be tried by 12 than carried by 6.