Such dead animals can hardly be found in large nature areas. Not all dying animals can be found in time. It's their natural behaviour to hide themselves, when they feel that they are going to die. Animals only have to be taken away when they can be found in time. A young stag, firstly found when it was totally decomposed An other selection of bones.
Small scavengers are also very effective in decomposition.
An animal, not died by a contagious disease will not be a danger for its other animals and man.