Long ago I was taught Chinto kata with the jumping kick as a jumping knee strike ( to get into the air) and the 2nd kick as the kick ( in the air ).
One day in practice I had hurt my knee and could not jump off it. Charles Murray told me, “Vic, that is no problem, just dial it back one level, and turn it into a stepping front kick, till you get better.” I did that and learned a lesson, that the technique contains layers of techniques.
In time this would become a useful training tool. It the more complex movement was beyond the student, the underlying kick probably needed work to get their basic technique stronger. Then working on the basic kick allowed them time to develop more strength for the more advanced movement.
Movement: Jumping Knee Strike Front Kick, Flying Front Kick
Back One Level: Left Step In Right Front Kick
Back Two Levels: Without movement Right Front Kick
This would serve to strengthen the individual for any technique.
Then when I learned Kusanku Kata, the same jumping knee strike followed by a jumping front kick was used.
And in the basics as I had been taught the jumping knee strike followed by a jumping front kick was the way we did it.
I did learn another jumping front kick from my studies in Tang Soo Do Moo Duk Kwan, a jumping front leg front kick. I remember showing it to Charles long ago. It required you to jump straight up and then kick with the front leg when off the floor.
I just practiced as I was taught and never tried to work other variations I would see on video tape.
Then move forward several decades. At one clinic Sherman Harrill showed us a specific application for the double jump kick. There he jumped into one person with a jumping front kick, kicking into their abdomen, then continued the jumping with a second front kick into the abdomen of a 2nd person.
I saw the use, and this was another variation for me. After time working on it, I saw the value of it and decided to incorporate it into our training.
I could see the value to both methods of kicking.
In Chinto kata we retained the jumping knee then jumping front kick, but there after in Kusanku we used the jumping front kick, jumping front kick. This change made very little difference in the kata, but preserved both methods of kicking.
I had made similar choices before.
When I was taught Wansu kata, the form ended with front kicks with the left leg. Mr. Lewis had told us they were originally lead leg knee strikes (as a parry against a kick) followed by a front kick with the same leg), but the kata had been changed long before (though I never heard why or where), Then training with several people in Goju Ryu one of the versions of Saifa kata I learned incorporated the raise the knee (parry) then use that leg for a front kick. And it was done with both legs in the kata.
I did not have to change what I was taught, I just incorporated that Saifa kata into the students training. For one thing preserving that method of kicking in the students curricula.
The thing is to develop the ability to do both in the karate-ka. Then these techniques become another layer to the arsenal.