Paradoxes in Medical Economics

When a patient with insurance is billed for a service, their insurance company negotiates lower prices for that service. When a patient without insurance is billed for a service, he has no negotiating power and so he ends up being billed for much more. And yet it is the patient without insurance who has the greater financial burden and who most likely cannot afford the higher price. Everyone argues that the uninsured patient does not pay bills anyway, but I have met many patients and families who struggle to put together money to cover their bills. These are the patients who we should be lowering our prices for; even if financial assistance is available, it makes so much more sense to me to discount things up front. Medical economics is a black box to me, and sometimes things don't make any sense.