If we're talking "kata" as in solo forms. Some of these have them, but are de-emphasized (Shuai Jiao). Others have "kata" as a two-man exercise of basic techniques (classic Jujitsu).
@Jas Key: Kajukenbo actually does have kata. There isn't a great importance on doing them well. As long as you memorized them. In other words, if you do the katas well, that's great, if you are just OK doing the katas, that's great also. The most important thing in Kajukenbo is passing the physical toughness requirements. But this is more in the traditional schools. We have seen Youtube videos from Kajukenbo McDojos, and the students are not tough guys. Bunkai was never emphasized in the katas. The katas that I learned, I did them well, but I was not good at memorizing lots of katas. Unfortunately, they were a requirement to be a Black Belt. By the way, I did NOT give you a Thumbs Down.
Kajukenbo has katas but whether you do them well or not is not a big issue. In other words, if you are good at katas, that is great, if you are not good at katas, that's great also. As long as the physical toughness requirements are met, such as you do not mind being in pain, having the wind knocked out of you, being bruised, seeing stars, going into shock, getting injured, seeing your own blood, etc.
Is Kajukenbo better because they emphasize physical toughness over being able to do katas well? Not necessarily. This is just the way it is in traditional Kajukenbo schools.
Everyone in a traditional Kajukenbo school has passed the toughness requirements. The beginning student in his first workout will be subjected to the above mentioned scenarios. The instructor and the other students are seeing how many workouts a new student can take before he quits. If a new student actually stays, we are all surprised.
I would say that if Kajukenbo emphasized kata more, there will probably a lot more students training in Kajukenbo.
What you are really asking is if there are any styles (instructors, really...) where you do not practice via repetition, or where you cannot go home and practice something. If you are hitting a heavy bag using some combinations given to you (or something you made up), then you are doing kata. Perhaps, not in the strictest sense, but if you are randomly flailing at a heavy bag, you are either not practicing anything, or you are letting off steam. Same for shadow boxing, hitting focus pads, air kicks and punches, working in front of a mirror. Repetition and solo work is critical to any martial art - traditional or modern, sport or otherwise.
If you are not practicing solo via repetition, you are not practicing your style. If you are not working on perfecting your technique, you are wasting your time.
It still confuses me how people do not see how both sport/modern martial arts and traditional martial arts just do the same thing under different names.
The secret is repetition repetition repetition. Drills, Kata, two names for doing the same thing, learning a technique and then repeating it. When you learn boxing you don't learn to throw the punches at random, you are taught the right technique for each in order. Jab-cross-hook-uppercut, repeat, Later on you learn to mix them up with foot work and defence tied in TMA works no different....