In America, price negotiation is done between providers and insurance carriers. This has a few obvious effects. First, it gives us the in-network/out-of-network distinction. Second, it introduces complexity in the math sense to pricing - providers aren't charging one price, they're charging a wide array of prices, although those prices don't really vary much.
The network thing also has the effect of reducing consumer choice in providers. I can use whatever doctors/facilities my insurance has in-network, unless I'm willing to cough up the difference out of my own pocket.
Of course, fixed prices would be that wicked socialist government control we're told is ruining everything.