This has been a personal interest to me, being a foreign language major (aaaaaagggggg) and I've written a paper or two at least touching on it.
There's actually lots of language learning software on the DS in Japan - there's training programs for the standardized english tests, and of course the Japanese-English dictionary software (which owns). I've been working on a couple text-intensive Japanese games, and there's definitely things I've picked up in games that I've been able to use (and also not sound retarded).
I think a dedicated, honest-to-god "game" would be great. I've been playing with Tadashii Kanji Kakitori-kun or whatever it's called. It still doesn't feel like a game but it's alright...