Often, you see in film, media, and photographs that patients are carried.. That's because prior to probably the late 60's/early 70's, (most) ambulance cots were not multiple level capable. They were 6 to 8" off the ground, some had handles to be lead with, some didn't.
If we have to carry someone, other than normal procedures, I'm a big fan of collapsible and folding stretchers. (Reeves, Junkin, etc)