You can't do that, either.I can only speak for TKD,
Yes, we do.we don't kick like that at all.
So does the front kick.This really close to the push kick to me. We kick with the ball of the foot and really kick out. In TKD, the kick that combine push is side kick. BUT side kick involves pivot of the hip to generate power.
It's hard? Maybe for you. Because people are different. A rear leg front kick should absolutely involve rotation.That's why it's about the most power kick in TKD. It's hard to pivot in front kick, it just doesn't have the power.