Long time taiji person here, and I will offer the sword player's view since nobody has. In the sword forms I teach, half the balance postures are one legged: du li with the sword extended, lifting the knee into a thrust, and so on. The sword is merciless about it. If your standing leg is not rooted and your waist is not leading, the tip of the blade wobbles and everyone in the room can see it. Empty hand hides weak balance. A 700 gram sword does not.
When I correct a student on those postures, I do not watch the lifted leg at all. I watch the standing foot. If the toes are gripping the floor, the waist has already checked out. My own teacher used to make us hold them with the sword for a full minute. Nobody shook in the leg. Everybody shook in the shoulders. That was the lesson.
That is what I think the taiji kick is actually training. The kick is not there to kick anyone. It is a balance exam you give yourself: shift all the weight into one leg without the shoulders tipping, extend the other leg without borrowing momentum from the torso, come back down without a thud. Do that slowly and the standing leg learns more than the kicking leg ever will.
On bent versus straight: in our line the knee stays soft until the last moment of extension, and even then never locked. I was told a locked knee is a locked kua, and a locked kua means the waist stopped leading. No idea if that is universal, but it matches what the sword tells me.
So my vote lands with the precondition idea. Longfist trains the kick. Taiji trains the person standing underneath the kick.