Unless of course you aren't conscious enough to direct the ambulance driver at all.
Imagine a world where prices are openly advertised, and as a result they start to drop.
Take laser eye surgery as an example. Prices are insanely competitive! They have been going down for years, and equipment manufacturers have been hard at work making more reliable and cheaper to operate equipment that has less side effects!
We have a free market for literally curing blindness and it works really well.
Now take more urgent but not life threatening cases. Last couple times I broke something, it was of the "well that sucks and it is kind of swollen but whatever" type, and I got to choose where to get an X-Ray at.
That is a perfect case where open pricing would drive the market price down and save me money.
As another example, physical therapy prices are often advertised on the open market. So are therapeutic massage prices. Both are price competitive markets.
Sure life threatening emergencies will still be subject to price gouging, but if the entire medical system is running more efficiently then even emergency services may see a reduction in costs in places. Maybe not for the trauma center, but for the hospital stay outside the ICU, why not?
I wouldn't have done said yes to that if I had known the price.
Or already know the price of how much it costs to get a bone set at different local providers and make your pick ahead of time.
Why assume people aren't going to shop around until something happens? "Hey ambulance driver, my preferred clinic is such and such take me there please."
Most medical situations are non-emergency.