Does health insurance need to exist?

I would like to keep politics out of this thread as much as possible please. This question is not about the ACA, but health insurance in general.

It seems that health care is one of the few fields that advances in technology and supplies(medicine), causes prices to increase rather than decrease.

What would happen to medical care if health insurance did not exist? Would prices of health care become affordable due to supply and demand? Would health care become more efficient due to treatment procedures dictated by doctors who went to medical school rather than insurance companies who went to medical billing school?