For the flying sutra, it's to act while in the transcendent state (which is what you experienced that one time--I've had that experience as well a couple of times, albeit more briefly--my body being this thing bouncing along within my consciousness, rather than my consciousness being within my body).
If I remember correctly, the overall reason for doing them is to keep yourself in that transcended state for longer and thus reap the hopeful benefits. Sometimes this was wonderful but most of the time the TMSP seemed to just blur up what I used to like about vanilla TM. On occasion though it was sublime. I remember once doing the flying on a big course and I had the most wonderful feeling of just floating down the room on a cloud, I looked round expecting everyone to be pointing at me and going "wow, he floated" but no, everyone was consumed in their own little world. I mention it only because it was a good lesson in the sort of mind/body coordination the sutras are trying to achieve. My body was doing it's own thing while my mind was expanded to heaven and beyond and really not taking part in the bouncing around. Now, if it was like that all the time, or once a week even! I would be living in Fairfield. Maybe it is for everyone there and I just got the spiritual short straw? I was pleased to stop doing it too, even though I still really like TM. Less is more maybe...
