Medicine is being talked about like a commodity, when in actuality its not like any other product. Do you want the best care or the best deal? They haven't started a cable channel for DIY medicine yet, or opened a Body Depot!
How would "competition" in the current medical system would be of any advantage to the patient. Competition would lead to efficiencies that would directly lead to a lesser standard of care, as none of the current healthcare sectors would stand for shrinking their own margins. Look to any other market for examples: you either get "less" product or it costs more!  Or you can go to Asia..
The only way to reduce costs in the delivery of medical care is to reduce or eliminate sectors (oh no socialism) that offer no direct benefit to the actual delivery of patient care! Ones that require a portion of each healthcare dollar to remain in business.  This would then leave alot of fellow Americans looking for work. Either way the decisions are difficult and outlook not rosy!