No they don't ... as Pack hunters they are very focused killing for food, not for other needs. The pack is set-up as a killing unit to benefit the pack as a group. Normally the Alpha males eat & gorge 1st, then primary females, then the beta females & the youngsters. The alpha animals will eat the organs 1st as they have the highest quality food benefit. You always need to remember that pack animals can make multiple attempts at a kill and not be successful.
The hierarchy of the pack is set based on many things none of which is killing to just get the prime meat. If there is waste laying around, in the eyes of mother natures predators, there was a disruptions to the kill site, or it was a solitary animal that walked away ... maybe a bear, bobcat, or the deer died for some other reason.
Whatever you have seen is not representative of a pack hunting order of canines ... please provide your qualifications or experience to identify wolf or coyote kills from other kill sites?
My only resource was my eyes. I have only seen about a half dozen kills, and 3 of them were left with over half the meat remaining. I dont know the circumstances behind their kills, and why they left them. It could very well been bears, I have many of them around me as well.
I also have an aunt that lives by Duluth, and they will kill her cows pretty regularly. Usually when they calf, the wolves take the calf, and if the mothers hang out, they kill the cow as well. They dont consume much of the cow kills, but what the MN DNR told her, is that they get spooked off the kill because of regular farming, and road traffic. Luckily the MN DNR has a program that will cover some of the loss from wolf kills, if they are determined by the DNR, that they are without a doubt, a wolf kill. Unfortunately that almost requires a video it seems at times, because fresh tracks all around the kill site just means, they came in to eat some of the remains, and that doesnt prove the wolf killed them.
I have came in counter with a few wolves in my day while in the woods, none of them have made any sort of a offensive attack on me, nor have they done as much as acknowledged I was even there. They had no fear of me, and treated me like a tree in the woods, walked straight at me, 15 yards away, I was feeling a little uneasy, I waved my arms, yelled, it didnt steer them from coming directly at me. I grabbed a stick, and threw it at them, and they veered about 20 yards into the woods, and continued to go around me. The wind was at my back, blowing directly to them. I was on foot, but I was about 5 feet from the back of my camper. They continued to the back of my property and made their way directly under my sons deer stand when he was in it hunting. They were following a pair of does, that made the same path minutes earlier. In the past couple of years, the wolves have moved down the road a few miles, but now the bear are getting over populated in the area. It is a no win for the deer. Its either hard winters, wolves, bears, or over generous doe tags.
Another encounter I had with wolves is from sitting in a deer stand in public land. The land was just logged a year earlier. I had seen 4 wolves in line, they were making a deer drive. Once they kicked up a deer, they would start yelping, and the posters would come in strong. After I seen part of this in real life, I had to do some reading on it. It is very impressive on how they hunt, I also know they are known to consume the majority of what they kill, but what I have witnessed is a little different from what I read. I know when I have wolves in the area, I dont see many deer at all. I know they dont kill all the deer, but they do drive them away.