The untrained dog, at best, thinks of itself as the alpha dog in the pack. In the domestic dog the pack consists of the people and animals that share the dog's territory. That doesn't sound too bad at all until you take into account that an alpha has the responsibility of deciding just about everything that the pack does, from defending territory to what and when they are going to eat. Take into account all the things in a man made world that a dog would not encounter in the wild such as cars and shops and laws. The untrained dog may decide that the territory has to be defended from EVERYTHING that steps foot within the boundary, which the dog has decided and you don't know, including the mailman, the local priest, your cats or next doors kids. The dog also has the responsibility of disciplining the pack when they do something wrong - think about that for a few minutes! The alpha dog also decides who leaves the den and when - remember this a best case.
Most dogs will simply be in a constant state of anxiety not knowing who is the leader, who is in charge and where the direction they crave is coming from. They will be unsettled, uncontrollable and destructive. House training is a taught behaviour. Walking on a lead is taught. Coming when called is taught.
Naturally the dog is a follower, it needs structure, rules and direction. It is not, as we are, always looking to be first, it is looking for a competent and fair leader and then it feels safe and secure.
It is, in fact, cruel to deny the dog this leadership and almost impossible to live with a totally untrained dog.