Well i mean there ARE ways to speed up one's own detox process, omho. For example one of the ways the liver detoxifies is by expelling fat soluble toxins in bile in the presence of high fat meals. Since bile is made mostly from lecithin and cholesterol when one eats egg yolks in massive quantity 12-24 a day, it can , in theory, speed up the rate at which the body releases stored fat soluble toxins. As for water soluble toxins, i'd assume taking in liquids, as most do on juice fasts, would cause most of the water solube toxins to be expelled through the kidneys.
Basically, yes, your body will automatically detox once your start eating right, however thats not to say that the process cant be sped up. In light of that though, if you don't have a heavy accumulation of toxins and symptoms to begin with then there may not be much of a need.
Another thing to consider is energy/bloodflow. One great point that's made clear in the raw food movement is that when your body is busy digesting all the time and repairing tissue it can't spend as much time getting rid of toxins. This is why many people in the raw movement advocate fasting in some form or another. For example i'm trying a liver cleanse where i'm having 6egg yolks in a glass of milk 2x's a day at noon and before bed. Of course one could argue that as long as your taking in enough nutrition that excess isn't really needed, which is a subjective point but a good one non-the-less.
Ultimatly it's up to you to decide what rite for yourself. A Low Toxin/Toxin Free diet will eventually allow the body to clean itself out, but it doesn't mean it can't be sped up. The real trick is to supply the body with what it needs using the least amount of energy on digestion as possible. Therefore experiement with foods and see how they sit with you. Perhaps raw fish will digest quickly and easily while raw beef will not digest as easily or vise-versa. experiement and see which foods fit your body well, and don't let dogma/idealism/image determine what you eat. Are you trying to meet the image/lifestyyle of raw paleo or are you trying to meet the image of health?
That being said, nutritionally raw beef and eggs are superior in every way