People try all sorts of things in the water - that does not mean those things are necessary for you to try and perhaps get frustrated over. If you want to explore body position and rotation, take it in smaller steps.
Can you glide for 10 seconds or so in Superman Glide (no kick)? Good. If you release your head, open the axilla (armpit) and focus on excellent posture (lengthen the spine, keep the shoulderblades slid down low away from the ears, let the chest expand to the side and suck in your abdominals) you will find you can glide further. When you pull one arm down and rotate into the skate position, you will likewise be able to hold that position for a few seconds without kicking. These exercises help you to hone your balance but ultimately you will be using your legs in some capacity to swim. You need them to help with hip rotation.
Rather than trying whole stroke without kicking at all, focus on quieting and keeping the legs straight and close together behind you. Taping the tops of the feet together with each switch is one way to do this. At some point you may find that the "kick" as you know it, isn't really necessary compared to the smaller positional shifts in the legs that I describe......
If you are having trouble doing any of these moves, you are probably bending at the hip or the waist and losing the strength and rigidity of the kinetic chain of muscles that join leg, glute, back, shoulder, arm. These drills will help you become more aware of that connection which is crucial.
I hope this helps.