Dancing Bear: The reason some folks leave the hide on the Elk quarters, sections or what ever is to prevent the meat from drying out, also for helping to keep it clean and in some circumstances to keep flies and Wasps from getting at the meat.
The Elk meat must be cooled (by quartering sectioning or hanging in a very cool spot) AND it also should be protected from drying out for to long a period of time.
I used to live on the west coast and "game meat drying out" was not much of a problem.
When I travelled to the high plains and the east slope of the Rockies to Hunt then the need to protect the meat from drying out was obvious and had to be done.
With Deer and Antelope I normally skin the carcass in a day or two and place it into my custom made muslin game bags for hanging (aging).
I also have special bags made for Elk quarters and depending on circumstances (duration of time to pass before the meat can be hung in a cooler or butchered) sometimes the hide is left on the meat sections for additional protection from drying out during the rest of the Hunt.
If you harvest an Elk and plan on heading home immediately or immediately to a butcher then I would skin it for complete and quick cooling and wrap it in game bags for protection from drying out.
As is often the case here on the east slope of the Rocky Mountains ones Elk may be in camp (in dry and very cool air) for maybe a week or more! I would leave the hide on the sections in this type instance.
I butcher most all of my own game meat and you can sure tell the difference between dried out meat and nice moist cool meat during the butchering process.
Where I live and Hunt a person can get a fresh slice of bread out of a bag and if you leave it exposed to the air you will have dry toast like bread in under 8 minutes!
You learn to eat your sandwiches quickly here - and to protect your game meat from drying out!
Cooling the meat is an absolute and keeping it from drying out is also very important to having better tasting game meat.
Hold into the wind
VarmintGuy