A huge reason hospitals lose money is due to the amount of charity care they provide. There is a saying that "Reagan instituted universal healthcare in the US, he just didn't institute a way to pay for it." That is, during Reagan's time, laws were passed that required hospitals to provide emergency care regardless of an individual's ability to pay. But no laws were passed then that actually funded that mandate.

So in rural areas where you have more people in poverty, if they had health insurance hospitals would be better able to actually collect payment for the legally required services they provide.