I can see why -- I've had the same terrible experience with billing shrapnel -- and I almost put a clause in my comment knowing this kind of response was almost inevitable.
What I did put in instead was that a lot of our details are different kinds of clothing on the fundamental incentives.
I strongly suspect that if you started a system from scratch around the central assumption that medicine should be handled as a market for medical products/services and the financing behind it should be private & for-profit, my guess is that you'd get very much the same thing.
The skill investment required for some interventions would lead to several consequences: required specialization to be effective, and a proliferation of specializations. Since the skill investments are costly, those costs are passed on in the form of high service rates. Few people know in advance which interventions they'll need, which makes planning for financing care risky, so an insurance market would develop. Insurers would have the same basic incentives to sell to those who are least likely to need their services, avoid those who are likely to need them completely, and independently negotiate their own payout deals with providers, which of course, varies by insurer, so few patients are going to be really sure how much anything costs even if they do understand how all the specialists interact in a given intervention.
And at that point, you have the recipe for the billing shrapnel problem everyone hates.
I find it difficult to consider healthcare a true market, since you get to find out the price/cost many weeks later. You generally have transparency over primary care visit prices, etc, but anything complicated is a total crap-shoot w/r/t what you'll be charged, by whom, and whether everyone involved is in/out of network. Ever have surgery? You get bills from parties you've never heard of all of them coming independently and its rocket science to even figure out deductibles at that point since there is no centralized ledger or central party to deal with.