Oh, I know. I've tried getting prices in the past. Traditional providers can't do it. One thing that has opened my eyes is using a Direct Primary Care (DPC) provider. I pay $75 a month for direct access to my doctor (email, text message, cell phone etc.). The access is great, but an unexpected side benefit is that a large percentage of their patients are un/underinsured. They can quote the prices for most common procedures from memory.
The other day I was getting a blood test and they asked if I wanted to bill my insurance or pay cash for it. I asked about the cost and they said "two-sixty". My response: "For two hundred sixty bucks we better bill the insurance. They laughed: no, $2.60 (it was an add on to another test for my physical). When I got home I googled pricing - the exact same test normally bills for around $65.
We do not have a free market. Other countries seem to have solid solutions for "socializing" medicine. I can't think of any highly functional system that is a free market. I don't even think that one is possible without people dying in the streets. Thus the best way forward is to try what has been successful elsewhere.