Two different things people seem to be arguing about - accuracy and usefulness.
Is describing balance-taking using vectors and forces correct? Yes. I completely agree on that.
Is it useful? Sometimes. Depends on the person and the situation. Sometimes understanding the theory of how something works can be helpful and can help you see what you're aiming for. However, I have to agree that it doesn't seem to be the most difficult or crucial part for most of us. Getting your own body to actually do it is much more difficult. And similarly, some of the most skilled people in many physical fields probably couldn't actually explain accurately what it is that they're doing. (E.g., how many of us can describe, correctly, why a bike stays upright when we ride it?)
I think of it as understanding with your body versus with your mind, or rather, understanding using kinesthetic and spatial processing functions of your brain rather than more abstract intellectual ones. They only help each other so much. OTOH it's not like they're 100% separate either so if someone finds it helps them to consciously analyze, why not.
I think that while its good to know the science behind aikido, it is more important to embody the principles of the art in physical terms not just in terms of intellectual understanding.
I could for example read a book on baking a cake, understand the theory, but unless I physically try and bake a cake,I would not be a cake baker.'Doing ' is the key to learning things.Theory is great ,however doing is better.Cheers, Joe.