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The only thing I (the furthest person from being a medical professional) could think make me want to lay someone prone is to ensure they don't choke themselves on potential vomit.
But there are certainly better ways to mitigate that than strapping someone face down in an ambulance.
It is a clearly stated rule in EMS that no patient is to be restrained in thr prone position and it has been so for a decade. Presumably this is because enough folks died just like this.
They used to "sandwich" combative patients between 2 backboard until that also was a no-no. >

It seems like common sense you'd never strap people down like that.  Not an EMT, I just think instinctually that's not what a reasonable person would do.