Shit, forgot about the rest of the hospital. How bout instead of an ER attached to the hospital, it's an Urgent Care attached to the hospital. Pay for the care, and off you go.
No pay, go find a hospital with an ER not an Urgent Care
This model is an ever increasing trend, but the laws regarding hospital owned Urgent cares make it difficult for the hospital to avoid violating what is called the "Emergency Medicine and Active Labor Transfer Act, EMTALA". There is nothing keeping non-hospital companies from opening Urgent Cares that require payment at the time of service, yet.
And as CT and laboratory technology gets less costly and more portable, this will be possible.
You will still need to transfer patient to the hospital if they require admission, or surgery. Of course, life threating illnesses like heart attacks, strokes etc, would need to be transferred to the ER as fast as possible.
Part of what prevents this is the mountain of regulations that control laboratory and radiology. The cost of licensing and inspecting a moderate outpatient lab is about 100k/year. But as the emergency medicine system colapses this will become a viable option.