Serious question...It seems like a lot of people's reasoning for doing the gutless method is to get the hide off to cool down the animal quickly. Wouldn't opening up the animal and removing all the guts cool it down much faster? There's a ton of heat in there.
I've done both but grew up gutting and I'm with @mtmuley and @Straight Arrow, I can get an animal gutted in about 10 minutes. Then start peeling the hide and breaking down the animal.
Seems like the best of both worlds and cooling it down much faster.
if cooling the meat asap is the only concern, nothing is going to cool a quarter faster than removing it and hanging on a tree nearby. gutting only slows the process of getting the quarters off. but even then, the differences are indiscernible in terms of how long it takes for spoilage to occur and the 10-20 minute delay in gutting. so it really doesn't matter one way or the other as long as you start field processing asap after death.
so, what it really comes down to, is whatever is easiest. to me it's obvious not gutting an animal is the fastest and easiest route to field processing. if you're not field processing and removing animals whole then yes, you absolutely need to gut that thing to help it cool off.