Taking a position requires time, and in action, time is of the essence. This is why you are not cutting in a position with the Aikido sword. Cutting is not done in stance, it's done on a support. Aikido action is structured and rhythmic by supports, not by positions.
The video uses kumitachi n°4 to illustrate this fundamental point :
The hanmi position is of the utmost importance in Aikido, and I don't think anyone would dispute that. Hanmi is the starting point, the origin of the spiral movement of Aikido, the triangular origin, which is why it's called the triple origin (sangen) :
But so much emphasis has been placed on the importance of hanmi in Aikido that we've ended up putting this position everywhere, including where it doesn't belong : in the movement itself. It's not there.
On the other hand, as soon as the movement is over, we systematically return to the hanmi position. If this were not the case, the next movement would not be able to start from the hanmi position either, and we would no longer be in an Aikido situation.
Every movement begins in hanmi position, every movement ends in hanmi position. This rule was laid down by O Sensei. What happens between these two positions is movement, and hanmi is nowhere to be found.
