The reason most martial artists study kata is because their teachers had them study it and so on back through time. Traditional martial arts have tended to emphasize "tradition" over innovation--as if martial art X was perected 500 years ago and the main task now is to keep it pure. Not very conducive to critical thinking.

The traditional Okinawan arts were built on tradition, yes, but a tradition of constant change. You can see how kata flowed from generation through generation. How new kata came into existence.

A large part of that tradition wasn't that the student changed things, instead the instructor, taking long personal expeience over decades, used that experience to direct their change.

Constant change but with directed intent.

The rule "THOU SHALL NOT CHANGE KATA" had no basis except as a tool to shape beginners. The instructors had the message, there really were no rules, but against the context of their lives, they first worked for advanced skill and then, and only then, worried about were other options required, and if so moved to fill that need.

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Traditional martial arts have tended to emphasize "tradition"

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One small step for critical thinking, one giant leap for fileboy.

On the few kata versus many debate:

Funakoshi did note that in the past masters may have only studied two or three kata and study them very deeply. He also noted that in recent years there had come a trend to learn many kata with no study just learning and practicing the sequence.
However the path he himself advocated was a middle ground: learn many kata moving on once a sequence was learned and performance was sufficiently skilled, BUT, after going through the curriculum one should return to the begining kata and study each in depth one by one.
This method gives the advantage of constantly challenging the students co-ordination and preventing him from being locked into patterns of movement while making sure that he is physically aware, fit strong and competent in his movements before begining deep study of fighting applications.

The 15 or 16 kata Funakoshi brought over were in my view a complete system. In his own words they were meant to give Japanese students an overview of all of Karate's movements and learning more kata would be pointless as one would just be replicating movements.

Later his attitude changed, but I think that methodology is quite ideal. It's why my own kata study has become limited to The kata that Funakoshi originally taught and one extra that I really like.

1st lets get an understanding there is a difference in Studying Kata and performing Kata just for Tourneys and Grading, or understanding each move or variation and just doing the movement, screaming and facial expression. After studying the applications in the kata, it actually becomes more like shadow boxing you are practicing how each application maybe approached and applied. It gets deeper and deeper.

But on a purely application base some of these techniques you could hardly ever think of on your on, and I find myself smiling of how wise these Masters were that they describe applicable techniques that apply now as they do then. Except now you would go to jail if you finsihed a combination in most katas.

Because the human body has limited weapon I'm also amused at how often you come across the same techniques thats found in the basic forms that you do in some of the systems founded Islands and nations away. Studying on your own is fine but then you only have your experinences and application to build from but input from 100s of years helps boarden your arisen though it chains you to a method early on.

I also have seen that kata is Universal communicator of Karate or the MA. It doesn't matter if the users are Japanese, Chinese, German, Russia, French, Iran, Korean or USA, you don't know each others language but start doing a Kata. And you all are near or on one page maybe slightly different version but commuicating and having fun if you are open minded. This understanding of kata expands to application and fighting spending the whole evening without missing a step enjoying each other without speaking a word of the others langauge. All though at the end of session you will pickup some common useage of the others langauge because you are having such fun.

Everything about the Martial arts doesn't require a cage or Octogon and gloves.