jss

Assuming we're only talking about solo-katas,
I think their value lies in reducing practice to the absolute minimum, by taking away the opponent. You do not have to worry about timing, the correct angle, ... You can focus on your movements and on any aspect of those movements you feel like focussing on. So after your body has learned the movements, you can focus on speed or power or foot placement or whatever. And the internal [suggestions for better word are welcome] qualities of your movements are all you need to worry about.
Of course, it's also possible to do your kata as a pre-programmed robot and learn nothing whatsoever. So as soon as you have memorized the kata, it is time to learn and practice the applications. And for these duo-katas the same thing holds true: you can practice them as a mindless robot or you can try to learn something.

And one other good thing about katas: you can do them all by yourself! If you have two weeks to prepare for a competion or something and you have limited access to training partners, better kata training than no training. (Question: better do kata training than conditioning? Depends on the event, I guess.)