Even if they did, I made my decision based on which provider I thought was doing to do the best job... I didn't know at the point I made that choice whether I would need those vicodin, so they wouldn't have been part of my decision. And once I was checked in to the SF General Hospital (after two hours of waiting) I was definitely not going to hobble down the street, trying to compare prices on vicodin.
Also my damn leg was broken. It wasn't really the right moment to break out Google Sheets and create an expected value analysis of my various healthcare provider options.
It's nice to say "if only we had more agency, prices would be lower"... but it ignores the fact you still need risk pooling (insurance) unless you expect everyone to keep savings for the worst case scenario. And pretty quickly a risk pool means someone has to decide how much that pool should pay to help treat a particular injury... and you're back to where you started.