I think most Japanese are surprised and pleased to learn of the extent that manga and anime have managed to make inroads into non-Japanese cultures of all sorts, but that has NEVER been an aim, per se.
Notice the way, for example, that Jackie Chan has a huge following in Japan. Who is Japan's Jackie for the rest of Asia?
He doesn't exist.
Beyond having the rest of the world paying for its steady stream of ingenious exports, in things cultural Japan is quite content for the world to just forget about them, more or less. And that's in spite of Hello Kitty's success.
A quick aside here --I'm no Bible Banger, but did you know that the percentage of Japanese who are Christian is lower now than during the freakin' TOKUGAWA era? Yes.
Exports of the cultural variety bring prying, foreign eyes. Japan tends to chaffe under that kind of scrutiny.
The peculiar brand of insularity that we see there is the polar opposite of that which prevails in France.
France - bring your genes here, leave your ways at home.
Japan - bring your ways here, but kindly take your honorable ass back home.