I agree in principle with much of what you are saying, but respectfully each individual and each situation is unique and what is best for one may not be best for another. I understand what 141 is saying... that there is a stronghold in her life and she feels fasting is the best hope of breaking it. I believe as she does that in her case she has a better chance of eating fruits and vegetables for 21 days if she first fasts. Fasting itself can be a very powerful means of giving us the strength and new outlook/fresh start through which otherwise overwhelmingly difficult change becomes possible.
To use a spiritual analogy, fasting would provide the swiftest and surest way to break the flesh and emerge into the spirit (die to the flesh and be born in the spirit) and then to be able to continue living in the spirit once going back to normal eating. Living in the spirit in this analogy would relate to one's ability to much more effortlessly do what is good and right and in this case specifically where discipline with healthful eating is concerned. Breaking the flesh while continuing to eat (and before a fast) will often be too difficult because there may still be too much of it (flesh) controlling us... and too often eating something, anything, will keep our irrepressible desires for wrong foods alive, where only fasting will destroy this.
I do agree that if what you propose can be done it is a good way to go, but certain individuals in certain circumstances are not ready to break bad habits without going all the way in denying themselves (fasting) and i openly acknowledge that i for one have been there.