I do KKW Taekwondo. While we use the older Palgwe forms (and actually a version of them only used by our school and one other school, to my knowledge), the Taegeuks suffer this problem as well: there are barely any kicks. We have front kicks in most of our forms. Side kicks come in our blue and red belt forms, as well as a couple crescent kicks at red belt.
Never in our forms do we do roundhouse kicks, back kicks, hook kicks, or pretty much any kicks at all.
In the kicking art. While it's been a while since I looked at the Taegeuks, I think you can do all 8 of them and do a total of maybe a dozen kicks. (Someone who does them can correct me). At our school, between the 5 basic Kibon forms and the 8 advanced Palgwe forms, we do:
- 44 front kicks (ok, so maybe quite a few of those)
- 8 side kicks
- 3 crescent kicks
- 1 back kick
This is all the forms needed to get your black belt. Each form has a minimum of 20 hand techniques, so aside from front kicks (which are fairly common) you have 8 side kicks, 3 crescent kicks, and a single back kick. These aren't done with the same footwork you will use for TKD sparring, and are not done in combination with each other.
Compare that to the drills we run, which feature:
- Different kicks, to include front kick, pushing kick, roundhouse kick, side kick, step-behind side kick, axe kick, step-behind hook kick, spinning hook kick, and tornado kick
- Different footwork, including step-through kicks, sliding kicks, jumping kicks, switch-kicks, double kicks, and repeated kicks
- Advanced combinations such as multiple kicks without placing your foot down
Now, part of this is the nature of Taekwondo as it has evolved away from Shotokan and TSD towards being an olympic sport based on kicks, without rejecting the hand techniques in the forms. We do train some of these kicks in our self-defense scenarios, (the fancier kicks are used a lot less, front kicks and roundhouse kicks a lot more, and often after grabbing your attacker's arm). But again, you don't see them in the forms at all.
I'm kind of curious what a Taekwondo form would look like if it sought to include all of the kicks we teach. But as it stands, those don't really show up in the poomsae.