Sadly, kata seems to have taken a backseat to modern training methods. This has to do with the belief that free sparring, bag and mitt work as well as other tools are far superior and more realistic. I find this view confusing because if we're talking about a street confrontation or similar situation, I doubt seriously that any thug I encounter is going to be wearing nothing more than shorts and MMA gloves or be heavily padded.
Kata training has been around for centuries. The koryu or ancient martial arts of Japan such as jujutsu and kenjutsu relied heavily on kata to practice specific attacks and counters in close-quarter combat scenarios that a founder of a given ryu (style) had successfully used in the past. The basic idea here is that if something worked before, it may very well work again. The key is in how kata is practiced.
If you know anything about kinesiology, you understand that muscles contract and relax based on thousands of patterns established in daily living tasks. Walking is a great example of this. We don't just jump out of the womb and stroll to the crib. It takes a long time for us to establish the correct patterns and sequences in order to walk smoothly and effectively. We make a lot of mistakes and fall down a lot. We also grow physically and mentally during the process. This is also true for anyone practicing kata whether it's partner-based or solo. Like walking, kata takes time and patience.
The problem with kata is many martial arts schools simply don't emphasize key aspects of its use. For example, the heart of karate kata is bunkai, which is the actual application of kata against a live opponent. If you are part of a karate dojo that does not practice bunkai, I would suggest your training is lacking a critical piece. In arts such as aikido or classical jujutsu, kata training allows for full-speed attacks and counters between students of equal skill and ability. The problem I've seen in many dojos is that students are not encouraged to provide a given attack with vigor and intent. The result of a lackluster approach to kata is poor technique and an under developed state of mental awareness. Having practiced aikido for many years, I can honestly say students of our art are some of the worst offenders. I believe this is what gives aikido a bad name in certain circles and it's well-deserved. We can't possibly begin to demonstrate the combat effectiveness of any martial art if we simply chase each-other around with an extended arm. This was not the way the kata was originally practiced.
The bottom line: kata training is only as valuable as the way it is taught and practiced. If we approach kata with the proper intent, that is, preparing for combat, it can be a very effective tool. However, if we study kata merely for aesthetics or just part of the training with a partner we will see disappointing results.
So, don't pay attention to sports minded or "real" combat players who say kata training is useless. They either haven't studied kata or were never taught how to apply it properly. Stay on your course and keep training.