I don't think it's nearly that simple. There's a great deal of competition in the medical industry for non-emergency care. (Emergency care has less but growing competition in the form of urgent care and emergency care centers not connected to hospitals.)
There are often multiple generic forms of drugs that are off patent. Even those on patent are usually not the sole (and sometimes not even the best) treatment option. One can, to a degree, usually choose their doctor. It depends on what insurance they accept and if they have room for new patients, but there are still usually options. This sometimes limits options for hospitals or other medical services to use, so it's not completely open like buying a loaf of bread, but demand isn't strictly inelastic and the buyer does have some possible choices.
Single-payer has the benefit of negotiating power, but that's still based on competition among pharmaceutical companies (presuming you don't get into price setting, which is problematic). The main thing keeping the insurance industry from negotiating lower prices en masse is anti-trust restrictions. There's been talk of lifting that by people on both sides of the aisle, but it doesn't seem to have reached critical mass just yet.