The Word of Wisdom does indicate that flesh is ordained for the use of man, but to be used sparingly. It is also pleasing unto God that they should not be used, only in times of winter, or of cold, or famine.--D & C 89:12-13
While many of us have heard and read these scriptures for years, let's not stop at verse 13. Verse 14 says that all grain is for our use, "to be the staff of life." Verse 15 says "And these hath God made for the use of man only in times of famine and excess of hunger."
This verse does NOT refer back to verse 12.
Grain, whole grain IS good for man, again not to be used in excess and certainly not to be used all stripped down to the point that the nutritive value has been depleted to the point of a simple carbohydrate.
The same goes for fruits. When the fruit is taken, stripped of the natural fibers and turned into juice, YES, JUICE, the end result is fructose, which turns to fat in the digestive process. When fruits are eaten, use small portions and eat them as they come off the tree (or plant.)
A low or no carb diet can be very beneficial, especially to the LDS culture. Atkins may not be the answer, but low or no carb lifestyles can be utilized without the excessive meat. How about more vegetables and eggs instead?