There is more than a little truth in what you say about why things changed moving karate to Japan.
But it wasn't Japan that forced the change, but the worldwide Depression. In the 20's/30's things were very hard on Okinawa. Many Okinawan's to survive had to leave and a worldwide disporia took place.. to Hong Kong, to Japan, to Hawaii, to Singapore, to South America.
Funakoshi, Mabuni, Motobu and the others were not working to make karate an acceptable study in Japan to fit into the Japanese society, but to gain acceptance to support their families and/or friends by making Okinawa more valuable to Japan.
Funakoshi, being an educator, realized making the names of the system more comfortable to the Japanese martial establishment, was a sounder way to integrate into the society. It was also accompanied with the reality Japan was walking all over their neighbors and was interested in Japanese arts, not say Chinese ones. So changing the names, even the kanjin for Karate, made sense because they were pushing an Okinawan art (not a Chinese one).
But Funakoshi didn't shy away from the origins and all of his book included sections of the Bubishi (in the original Chinese).
So at one level he was helping make name changes, but at another level he never hid anything.
His changes worked and the practice did get integrated into elite education (university). BTW Karate was not for the masses on Okinawa, and where he took it was to the youth of the Japanese elite.
Today, Joe Swift has told me, very few people in Japan realize karate isn't pure Japanese. At the same time the study of Karate in Japan is still a small time event. Most Japanese don't do the martial arts of any sort.
What Funakoshi really did was craft a group of Japanese instructors very quickly, and they were the disciples who spread his karate. He was older (alas something I know well) and it of course was impossible for him to teach in all those locations. Those instructors (including his son) were insturmental in changing Shotokan from it's origins. Who knows how much a hand he had in those changes. Some of which actually came from some of them training in China and importing techniques (such as kicking techniques) to be added to Shotokan. So the Japanese Shotokan stylists didn't shy from China (Of course they were occupying it then, and his students were often officers or occupying administrators -- after all he taught the elite).
Among the earliest attempts at Japanese control was the famous 1930's meeting to 'force the naming' of Karate back on Okinawa. After WWII it became more obvious. Japanese dogi were used for uniforms. Rank and belt structures and organizations came into existence, paralleling the earlier Japanese experiments.
Today, in austerity moves, mainland Japan has crept into funding public events in Okinawa, and the spectre of mainland karate groups may be trying to control Okinawan karte, simply becuase they're working hard to gain Olympic acceptance, and still want those 1930's dreams, only a common 'olympic' karate for everyone.
These events are much more complex and involved than these few short words indicate. None of them require or want our comments, btw, just as most of you don't want theirs.
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