Indeed. The only reason is that kata speed up the process, by pointing out the stuff that works.Then why not drill simple movements and even have students make their own kata? ( being devil's advocate)
You can in principle reinvent all math from scratch, but you will take a lifetime and end up inventing the same math that you could learn in a few years, maybe with different symbols and names, but essentially the same.
The same is karate: human biomechanics is human biomechanics and the way you use to your advantage are already there. So it's just faster to learn them directly rather than reinventing them,
But the exercise of taking a solution and encode in a kata is a very good idea.