Definitely true in terms of specific, exacting judging on the particular style itself.
Where I diverge is that there are varying stances within a style which accomplish certain & differing objectives. This dimension of stances exists across all styles of karate and among the traditional martial arts as a generalization. There's a horse stance in the fung fu's as a whole; there's a horse stance in Shotokan. There's a front stance in Tang Soo Do and there is a lunge stance in Shotokan. Some particular & specific variations which do exist between style, the are commonalities, common objectives. The later area I can pass some competent judgement on because of my participation and experience in traditional karate and martial arts.
Here’s the first place we can still run into issues. I guarantee the jigotai/horse stance I teach is incorrect in most other styles. It’s not low enough, and usually not wide enough. How can someone from any other style know if that stance is correct or not? If I judged their stance on my teaching criteria...
Sure. Even at the expert level, no one is all knowing. Everyone puzzles over particular kata routines and what the author-masters were seeking to convey. This is the old, anti-karate argument that one really doesn't know what the kata is for or what it's trying to do. Because we are hundreds of years removed, with many interim masters, of course there is truth to that criticism.
Yet, this can be sad to be a criticism of traditional martial arts, traditional karate's as a whole generalization. The answer comes from realizing that the human potential sought to be developed through traditional martial arts training addresses comprehensively the strengths of that human potential. And that's spelled out in the manuals, the curriculum.
The other sport, physically centered methods such as boxing IMO are more integral in their design, they are easier to see how the whole system works and more practical to train. But they don't share the broad based strengths that traditional martial arts does. This TMA character is embodied in the major components of traditional karate training, kihon, kata, kumite. This character is the essence or soul of what we are looking for then, in kata.
Furthermore, the way in which traditional martial arts seeks to develop this broad-based human potential is inherently different that how boxing or wrestling's more physically centered method. The characteristic training form and practice then will also be inherent and expressed in kata.
Traditional karate - whatever the style - becomes powerful & effective when we understand and train to it's universal underlying principle aimed at the above. Hence, our kihon , kumite & kata done properly to form & intent will reflect this essence in our performance.
BTW: My interpretation then, would handle the performance art criticism of kata.
I don’t know that we inTMA have as much more depth than some other sport/hobby activities. If someone trains with a coach long-term in any discipline, that coach can have that kind of lasting impact on character. We occasionally see it from high school sports coaches, when they have some of the same players for 3-4 years. That said, I think we do tend to be more purposeful in that area than many in other disciplines, so maybe we are more generally effective there.
As for the depth of the kata, I’m not convinced. My kata aren’t that deep. They aren’t intended to be. They are physical exercises to engrain some transitions and make solo practice more organized. They are not much more than that. So, the soul of my art isn’t in them. If someone wanted to make them prettier for performance, I don’t think there’s anything to criticize in that pursuit, except maybe their choice of a base to start from. As long as they don’t confuse the performance art practice with martial practice, it’s all good.