I can't find any responses to your question so I'll take a stab at it. Your question is, "why eliminate foods only to reintroduce them later?" Your initial conclusion is that, if you eliminate a food that causes, why not just stick to that program. That is a great question.
As I understand it, not everyone has issues with all the elements of the FODMAP program. For example, you may be be sensitive to sorbitol. If that is the case, you will likely not be able to reintroduce blackberries into your diet. Same holds true for other FODMAP groups.
I am following the elimination diet right now and can assure you that after my initial 6 weeks effort, the first thing that I'm going to reintroduce is bread. I certainly hope that works because I am good baker and thoroughly enjoy bread. If adding bread works, that will be great; if not, I'll learn to live without it. No big deal either way.
I hope this helps you understand the process. The elimination phase doesn't have to be forever ... just long enough to clear your system and see what works for you. Try to not look at the elimination phase as a limit on what you can eat for the rest of your life; rather, as a way to identify those things that work for you and those that cause problems.