At our dog training facility in Northern Virginia, we are big advocates for teaching as many different positions to the dog as possible. This is done in order to have a useful command based off of the scenario that you are currently in.
The sit command has many great benefits! For example, we use this daily for door manners. Additionally, we use the sit for every day obedience training while working the dogs when we only plan to leave the dog in a command for a short amount of time. You will see this done in literally hundreds of our YouTube videos. Also, we often times use the sit command for allowing people to calmly and controllably greet the dog, as well as using it for food manners (making them wait for their food until we release them).
The most advantageous purpose of the down command is the ability to leave the dog in a position for a prolonged period of time and the dog can relax and be comfortable. Anytime I plan to leave a dog in a specific position/spot for more than a minute or two, I will always down them.
Stand is one of the most underutilized and least thought of command; however, we use it on a daily basis! The great thing about the stand command is that it makes grooming your dog so much better and easy! You just tell them to “stand” and then you can groom them, brush them, give them flea medicine, etc. It’s a command that every groomer in America wished every dog they worked with knew!
Also, I am big on teaching the dog to “transition” through all of these commands; meaning, telling them to down, pop them up into a sit, then to a stand, to a down, etc. So, they learn to transition among the commands.
Many trainers and owners teach the commands independently; however, they do not teach the dog how to actually “transition” through the commands.