This was one of my pet peeves with the training I had started with a long long time ago - the basics we were learning were not related to the 'self defence' techniques, which in turn were not related to kata, and certainly did not filter into the sparring sessions. This made me ponder the martial arts long and hard and frankly I nearly threw the towel in a couple of years ago when I got tired and bored of this empty training.
I reiterated this point to Mir (from Going My Way) when she saw me sparring in the States end 2006 and thought it was a fantastic demo of skills -- she was extremely generous, but I told her that kind of sparring was really more prancing around throwing a few kicks and punches to some really nice opponents. Truly not a very serious demonstration of skill level.
To be fair I certainly think there are clear and communicable skills that traditional kata theory does teach for sparring. There are also takeaways from sparring that can be in turn brought back into kata practice. This is what Dan indicates when he ask "... is whether kata alone is sufficient for realistic defence. The answer would be of course not." But I think that it is far from common to have modern sportive practitioners with an equal distribution of skill which goes from one area of their training to others.
A lot of skills are honed by the overlap in training methods. So when I train my students kata, I'm also communicating to them essential skills needed for combat/sparring/self defence. A case in point - several years ago I remember asking two young students trained for about a year with us what is the most important thing they learned from my school. They replied the most important thing was they learned how to tuck their chin down, protect their noses, and lead with their foreheads. They said that they used that skill both in basketball and football in order not to catch balls with their faces!! :-) And yet these two young gentleman never started their sparring training with us - this was only from basics and kata!
Traditional Taekwondo Technique Workshop