First and most importantly, kata lacks resistance in its training. Everyone performs better when there is no pressure. Simply because you do it well in the air doesnt mean that it will be so in self defense and that can be dangerous.
This is where many people get stuck at...
Kata isn't meant to be solo practice in my opinion. It's merely the beginning stage of kata practice.
Maybe it is because of karate and TKD's fast expansion due to introduction to the educational systems that this important part of training got overlooked?
One of the merits of kata is that it can be practised to certain extent alone. However the further training of kata (bunkai oyo) needs a partner.
But in the unfortunate situation of a fight, the chance that someones opponent knows that he/she's applying principles from kata are very slim. I wouldn't even stick to one kata's principles per se, because I know a couple that have great techniques and principles suitable for mixing up.
Which will leave an opponent guessing (about what happens or in the rare occasion about what kata).