Beyond the legal aspects, I can't even imagine having a dog hunt deer, elk or antelope hunt with me. Every dog I've ever had will react to the scent of a deer or elk. Also what about when it decides to chase a squirrel when you finally see that once-in-a-lifetime 195" buck and you are trying to lay low.
You have issues with the dog's scent. The dog's added movement is a detriment, since deer and elk pick up movement like crazy. There is the added noise of a dog that likes to bounce around checking scents.
The one thing I have seen a dog useful for in big game hunting is hounds for bear and lion or a dog to track a wounded animal.