I get that. For me, as a Japanese American, my perspective is that Japanese cuisine and Chinese cuisine, while they may share commonalities, is actually quite different (again, totally my personal perspective, YMMV). I think this is especially true during the time period that Karen was supposed to be representing. Japanese cuisine was starting to be influenced by Chinese cooking, to be sure--and noodles are an excellent example of this--but the application of how noodles were used, and the overall flavor profiles were very, very different (also very different based on what region we're in as you've mentioned, and rural home cooking vs. the highly formal meals at court.
I think that's why even though I really like Karen a LOT, I'm fine with Jeremy staying over Karen. Jeremy's dish was a decent dish fit the general parameters, but was too fussy and skimpy; Karen's dish missed the point entirely, because she got swept up in the idea of Chinese influences and got carried away cooking the Chinese food she wanted to cook in the first place. (Also, that soup looked kind of gross to me, but of course I have no way of knowing how it ate). I'm hoping she wins LCK, because I'd love to see her back in the competition.
FWIW, unless I was seriously in-the-know on Japanese cooking, I mighta shied away from the Imperial Japan flag...that would have intimidated the hell out of me! I kinda assumed they were talking about imperial court cuisine, which traditionally would have been served in a series of small dishes balancing a variety of flavors and textures presented with refined, minimalist beauty and representing an overall harmony and balance over the course of the meal. To try to capture that in one dish? If you've never done it before? Whew! As soon as Karen chose the Japanese flag, after grumbling about not getting to cook Chinese food, I looked at my husband and said, "Karen's going home." I think someone who is really into it could seriously knock it out of the park and win, because it's a reflects a lot of technique, refinement, restraint, and artistic presentation, but it was just not the right flag for Karen.