What we have today is a large number of people over using emergency rooms. And ending up in ERs because they didn’t get basic checks ups when the problem was small. Yes, some of them are illegals, but many of them are just folks without insurance.
Actually, a lot of over-utilization of the ER comes from people with employer-paid health insurance. If benefit levels are lowered for ER claims, patients go to the ER less and yet still go when they should (they just don't go when they shouldn't). People with health savings accounts utilize the health system at a lower rate than people with employer-paid benefits (though they still have health as good as those in employer-paid plans).