Even a large percentage of ER visits would likely see people acting with price sensitivity -- This is why in some places of the country you see Emergency Rooms advertising about how low their current wait time is. The wait time isn't really relevant to true emergencies (you get seen right away), but people without true emergencies don't want to wait. Financial cost is irrelevant (someone else is paying), but the cost to their time is relevant, and so people select emergency rooms (and urgent care clinics) where they will have to wait less. Hospitals are acting on the one thing that the patient cares about (sitting in a waiting room), since the other (price) doesn't matter.
For the really expensive things, like end of life care, governments with universal healthcare systems are the ones that act with price sensitivity and ration this care and refuse in some cases to pay for the most expensive treatments. For example, the UK has the National Institute for Health and Clinical Excellence (NICE), which set a maximum of about $47,000 per quality-adjusted year gained. What we refuse to do in the US is allow patients to make a choice like that (instead, we mandate that insurance cover far more in health care expenses, driving up the cost of that insurance). As a comparison, the US sets it supposedly to about $50,000 per QALY, but in practice it tends to be far more, with some regulation-required treatments requiring as much as $500,000 per quality adjusted year (some heart pumps, and kidney dialysis being another very expensive example).