Let me speak here with my own words and what Kase has written and talked about.
First of all the hikite (pulling hand or when its jammed into the hip) is very important and is not to be neglected, its a part of our system.
Beginners starts with large movements (O-Waza) because they simply need to build the necessary muscles and learn to coordinate the movements perfectly. This allows the beginner to gain maximum speed and power in a natural way because the movement is long especially in Kihon. That is way we have long movements in Kihon like "Oi-tsuki". This is very important that you build up your body and strenght up to the level Shodan before you are ready to move on. As you proberbly noticed big movements like Oi-tsuki is not realistic out in the street. So the big movements are there to help build up power.
"Taiji Kase describes this phase of development as an elementary school and point out that it is a very important step in the development, which should be studied carefully with lots of repetitions by both beginners and out of those who have trained very long. But there's is no reason to spend rest of their lives in school!"
So what does he mean by this? Simply that there is no point to get stuck in the training rest of your life and only do elementary karate (Karate that is based from the hip, i'm talking about your hikite to start with).
Kase had especially studied the open hand techniques for over 20 years of time. He also intergrated techniques from Kendo (Jigen-ryu, Ni-ten ichi-ryu) into the karate.
When the student have reached a good level, it is not always necessary to use the largest movements in the moment to achieve maximum effect. The goal of these exercises is to achieve the same effect and force of all the techniques without thinking about each movement begins or ends.
By leaving the hikite-karate at one point, you can move more freely and more independent of your arm positions. This will open up your mind. Your techniques become more realistic in defence and attacks. This can be amplied into kihon, kumite and kata exercisses. You should strive for developing maximum power from any range and position no matter were your arms are.
When opening up hikite this will open up new areas like: O-waza,Chu-waza and Ko-waza principles which in turn can be added into kihon, kumite and kata. So my advise is, if you have reached up to Shodan or beyond it's time to start think about what you are doing, you may have som benifits from it. By using large techniques, mid-range and small techniques combined togheter we can get a very good system of defence.
I give you an small example that you can applie and try out . Llet me know if you have improved or not.
Lets keep it simpel, we take the kihon kata: Taikyoku Shodan not a impressive kata, not a very realistic kata. Only meaning is to build up our muscle and spirit.
To make Taikyoku more realistic and more challenging lets add som hen-te (same hand does more techniques).
1. add more techniques to every block and attack in the kata (1. technique gedan-barai to left and with the same hand Chudan-tate-uke) now do that in every part of the kata that there is an gedan-barai
2. in every Oi-tsuki do instead: Oi-tsuki+Jodan Ura-tsuki+Chudan Tate-tsuki.
3. to spice this up do it "Go" backwards and suddenly you will have an very realistic kata, ok still very low stances but use your mind and adapt it even more.
4. Now when doing this kata try to forget your hikite hand just let it hang straight down relaxed, just a bit kime to hold the arm in place.
5. for the advanced when done the blocking and attacks with the front arm add a Chudan or Jodan Shuto-uchi with the back arm.
6. By now the kata should be very challenging and good work out. Also a mind opnener.
This is what you can do when you not think about your hikite but its still there waiting to react...