Kanku Dai

In our recent, advanced kata, sessions we've been practicing kanku dai. My instructor, sensei Mike (5th dan IJKA) explained that there is no half step when performing the first keage, but there is when performing the last keage. I took issue with this saying it was incorrect. I want to apologise for this course of action as it is inappropriate to make such comments to a senior instructor. My instructors way of doing the kata is as follows:-



My understanding of the kata is more in line with the common accepted norm of moving the back foot on the first keage and keeping the back foot still on the last keage. As per:-



I then discovered this video with Osaka Sensei performing kanku dai under the watchful gaze of Master Nakayama. Surely, with the half step for the first keage and then no step for the last keage, with sensei Nakayama watching, is correct:-



Along with Sensei Kato and Sensei Kagawa doing the the same:-





I then came across this video of who i believe to be K. Nakaya. In this video, there is a step in both keages:-



There is no doubt that the common standard is half step only on the first kick. However, think about this for a second if you will? This doesn't make sense. From the point of view of generating speed and power, you must pull your foot in when executing the keage from kokutsu dachi. If you do not, then your kick is much slower. However, from a training point of view it is perfect to make your student kick from kokutsu dachi. He must ensure his back stance is sufficiently weighted towards the back leg in order to kick smoothly. Was this Master Nakayama's thinking when writing his 'best karate' series?