Hi Tarik, I have almost the same experience as you-
My daily practice should be a set of basic movement exercises and it sort of is, however, I don't always do all of them formally, although I do parts of them whenever I am standing and waiting.
I am constantly finding extra unnecessary tension in my structure, typically in the hips and shoulders, that is held habitually and when released, reduces the effort needed (and in some cases, pain) to achieve the same posture during movement or stillness and this also increases my freedom of movement and ability to affect my surroundings with significantly less effort.
And, I think everyone can agree this (2nd part above) is desireable from an aikidoka's point of view. It just turns out (once you start really focusing on it) that relaxing unnecessary tension is really hard! It is a rewarding pursuit and a good way to practice during the day, every day.
Now, I really would love to hear what your eye-opening experiences were. Please share if you feel comfortable. Although it is probably right to make a new thread. Thanks!