I believe that kata exist because written descriptions of martial techniques were not practical, probably for three reasons:
- I can bear witness that it is very difficult to describe martial motions in writing, and I think it would be even more difficult to do it using Kanji. Funakoshi's first attempts to describe kata movements in writing were terribly inadequate. It may have just worked better to teach students a dance instead.
- Add to the above the fact that most people would not read and write, and written instruction became even less practical. Everybody could dance, whether literate or not.
- In at least two situations (Okinawa under Japanese rule, and China after the Manchu invasion), being caught with a martial-arts manual would have been a deadly mistake. Dances were more secure than written manuals.
Certainly the practice was widespread in both Okinawa and in China.
Note that "recent fighting systems" are documented using technology that is very new compared to karate. Specifically, modern fighting manuals rely heavily on photography, and the even-more-recent ability to reprint photos in books. And of course we use digital video now, which is somewhat new even to us. The ancient masters didn't have any analogous means of illustration. Illustrations of martial technique from the period are weirdly stylized and not very informative.
So, basically, dances worked better as a vehicle for preserving and transmitting knowledge.