For ER, co-pays are not needed. Doctors can mostly see if the patient is in need of their care. It's the actual doctor visits that need them tbh. Nothing will stop people from going when their head hurts and all they need is over the counter aspirin. Going to the doctor will cost the system for each visit.
Co-pay doesn't have to be expensive, could be like $20ish. Serves a bit of a deterrent for unnecessary visits. If te person can prove he/she can't even pay the $20, it can be waived or billed later.