We used to have dogs that would eat shit when I was in the greyhound business. There would usually be one or two in every kennel. I never could figure out why they did it although some say it is a vitamin deficiency but with all the supplements those dogs get I can't imagine that is the cause. I would have to constantly stay in the pens to scoop poop as soon as it hit the ground or the one or two shiteaters would have at it and nothing would stop them either.
If they did bury their faces into a big pile then it would be stuck to the front of their muzzles and on their faces as well. I would have to clean it up before they wiped the muzzle on other dogs or walls or whatever. Some dogs learned that you would pick it up fast so they would stand at attention at another dog's butt and try to catch it before it fell to the ground.
I had a trainer tell me once he had a dog that loved to eat shit more than actual feed (which looks like cabbage roll stuffing once it's mixed by the way). He said he took a feed pan full of food and a feed pan full of poop and put them both in front of his dog and the dog ate the poop!
I remember a AA 3/8's dog (very good grade) whose name was Poopieotzie. They named him Poopieotzie because he loved to eat shit and he also liked to roll in it. The trainer laughed when I asked him about it one day. He said as long as Poopieotzie continued to earn money like he did he would gladly give him a bath everyday as long as "rolling in the poop kept him running.