Health care that is not time critical should not work like the fire department. In fact, emergency rooms, once they diagnose something as not being an emergency should be able to say, "sorry, this isn't the right place for this, go to a doctors office."
With non-emergency care we should all be able to get price quotes up front, we should be completely aware of our choices and the be able to shop around. We could maybe outsource that to health care clubs like Aetna and UHC if we choose to (knowing that we are getting less choice and that we'll have to deal with those bureaucracies as a trade-off), but there shouldn't be any tax breaks or employee incentives for using those health clubs.
I recently had surgery to have my vision corrected with no "insurance" (or health care club) involved and it was so nice. I shopped around, the doctors all competed for my business and treated me like royalty, there was absolutely no confusion over price, there were financing options available, the technology was cutting edge (or I could have chosen to go less cutting edge and paid less), it was incredibly refreshing. I'd love if most of my health care could be like that.