They shouldn't get the free ride they're getting. If you are uninsured or underinsured, but have some resources, the hospital will come after you for everything you have. If you don't have anything, they just write off the cost of your care and let it slide.
I was uninsured/underinsured for about a year and that was the one time in my life I needed surgery. Dealing with the billing was insane. Things that went through insurance were about 10% the cost of items that weren't covered. It was bizarre and illogical.