I've always wondered why in nearly all the styles katas/forms I've seen or done there isn't more kicks, I can't recall seeing a kata with a roundhouse kick at all never mind jumping ones. The only kicks I've seen really are basic front and side kicks. Seems odd to leave kicks out in any style really let alone TKD.
The kata, and forms in related arts, were originally recordings of combat-effective techniques, and high/complex kicks were just not part of the arsenal that people like Matsumura, Azato, Otosu, Peichin and the other Okinawan karate pioneers used as fighting methods. Motobu in his writings makes it clear that the kata were regarded as fighting styles
themselves, rather than being mere
components of separate arts. The lack of complex kicks suggests a suspicion on the part of the early karate masters that such kicks would be useful at the typical fighting distances of violent civilian encounters—their preference seems to have been, train techniques for close quarters, and the katas, as records of those techs, would inevitably show very few kicks.
It's interesting to see how this changed, but not very much, as time went by. If you compare the kata Empi with the Korean borrowing Eunbi (even the name of this hyung was left essentially unchanged), what you see is that certain leg strikes that were based on the assumption of CQ combat, involving nasty groin strikes and other techs based on closing the distance, have been converted into a stylistically preferable high kick. Take a look at the
bunkai Paul James offers for a certain recurrent movement sequence in Empi. In Eunbi, those knee strikes James illustrates are replaced by high front snap kicks, with the knee strike reinterpreted as merely the chamber for those high kicks. The Empi leg movements make complete sense at the close range the combat assumes, in the context of the associated hand techs—but the high front snap kicks in Eunbi are seriously problematic, because they imply a fighting range that doesn't fit at all well with the kind of close-in attacks that the bunkai for the hand techs represent.
So what you see seems to be a kind of progressive revisionism with respect to the original Japanse forms and their combat interpretation, in the direction of more acrobatic and stylized interpretation of leg movements. Even so, the majority of movements in virtually any of the classic TKD hyungs are hand/arm techs, a legacy of their sources in Shotokan, or in a few instances, still older versions of karate. Those new hyungs that we saw videos of quite some time back, or the Chloe Bruce type performances, show the next phase of this process, with the CQ combat content replaced almost entirely by acrobatics....