Very good points for sure. I never would have thought that people would pay for bills without insurance. You are definitely a rarity.
I think a lot depends on the demographics in the hospital service area. I know a number of people who set up payment plans for care recieved and proceed to pay for the services (with interest) over time. What this area does not have is a large contingent of illegal aliens, and the population of the region is predominantly caucasian, with no 'inner city' demographic to speak of. The poorest are covered through Medicaid, there is BIA health services, and there are insured folks, too.
If you eliminate the demographics most likely to skip out on a bill, (especially illegals), I think you'd find the percentage of 'uninsured' people who pay cash or make arrangements to pay off their bill over time would increase significantly.
It is, however, grossly politically incorrect to mention that concept, however worded.
Many areas have dire problems because the concentrations of nonpaying demographic groups are relativley high.
A reasonable degree of border enforcement might have relieved this situation decades ago.