Because dynamic stretching serves the purpose of increasing the maximum point at which you can stretch your leg, and kicking is focused on the technique of kicking. If I want to work on my front kick, I will do a stretching axe kick for the stretch, and then front kick in order to get the kick in. I guarantee you I get more of a stretch out of the swinging motion, and my stretch kick can go higher than my actual kick.
Same thing for side kick or back kick. I will swing my leg up for a stretch side kick, I will chamber and push for an actual side kick.
There's other motions as well. The motion for a stretching crescent kick is a wide sweeping motion, where I'll use a quicker, more targeted motion for an actual kick.
The muscles stretch differently when you do a swinging motion for a stretch kick than when you chamber and snap. I don't really see how anyone can do a front kick and then an axe kick and go "yeah, the stretch feels the same." Unless you're doing one of the kicks wrong and both look the same, too.