This is truly a complicated issue. Air versus ground depends on injury, population density, central place distances, regional economics, etc.
The bottom line is air was primarily introduced, by hospitals, to fill beds. The good old profit motive. The cost of the transport is easily offset by the cost of hospitalization for traumatic injuries.
I know, on a personal level, that if you are injured and hurting you want to get to the hospital as fast as possible. A 10 minute helicopter ride seems far more preferable than a 50 minute ride on rubber tires. I will say, in some of the moderately remote areas I've worked, if the ground ambulance crew headed straight for the hospital their enroute times are comparable to the time necessary to transfer from the ground ambulance to the air ambulance and then transport.
I guess what I'm saying is that, studies aside, if hospitals profit more from using air transport there will always be a place for HEMS.