FWIW, that's not necessarily better. In some cases, when suffering a crushing injury, it's best to leave the crushing weight in place until EMS personnel arrive and can transition immediately from "removing the weight" to "corresponding intervention". You can see a bit of the discussion around what goes into treating "crush" type injuries here:
https://www.ems1.com/patient-handling/articles/4-things-ems-...
Also, as others have pointed out, it's probably best to lift the car off the patient as opposed to running them over with the wheels a second time.
Would you move forward or backwards? How sure are you'd get that decision right?
Would you be confident that you weren't going to cause further injury by moving?
Would you be confident that you weren't creating further legal liability by moving?
My point is that I'm not sure a human driver would always move the car - or whether moving would always be the right thing to do.
Can't wait to when we get off this dumb fetish. The robot car of the future is a golf cart, or a kei car, or a battery powered rickshaw.
(* since this always come up, let me emphasize, for the _city_. fur trappers can keep their cars)