hmmm, thoughtful question, because as you say, sugar is "crystalized" in form... but if you think about it further, that is really all there is to it. I don't think sugar exists in nature. Sure, sugarcane does, but white crystalized sugar is man-made. Salt, on the other hand, is part of the earth. Salt is also part of the human body, and a necessary mineral. Sugar is not. Salt draws toxins/negativity into it -- it is yang in nature. Sugar is expansive, it is yin in nature. ... all this, and not to mention, sugar can get sticky... and attract ants!
One could argue that you can "cleanse" with whatever you want, as long as you set the intention... but I would say certain elements -- and litterally, the Elements -- water, air (burning sage), fire(exposure to sun/moon light), and earth (salt / burying in the ground) can greatly assist. And... would you wash your dishes with honey, simply because it looks like amber-colored dishwashing soap?