In reality cash paying customers should get a discount. A) they're paying right away rather than sometime in the future like insurance company payments, B) there's no need to run it through a billing/coding service.
My brother, while without healthcare, did need to get some services done. Through the traditional art of 'bargaining' and solemn ceremony of 'cash on the barrelhead', he was often able to obtain discounts of half the price over even what the insurance companies paid.
The trick is that such works better for small medical providers - hospitals often can't even give you an estimate of what a routine procedure is going to cost ahead of time, they're so stuck in the 'figure it out later, and just bill insurance' mindset.
During that time, what basically happened is that he was put in touch with what I'd call an 'cash friendly informal network'. IE the doctor who accepted cash told him where to find a lab that accepted cash, so on and so forth.
In the end, I hate to say it, but between copays, deductibles, and everything else, my brother *probably* managed to get a broken arm dealt with cheaper than what the insurance deductibles would have cost him.