Well, there was a general tend towards westernization in Meiji - but I can't think of any of Sokaku Takeda's students who were actively or primarily interested in the cultural elements. In fact, Sokaku taught mostly short workshops with people who were primarily interested in the practical martial elements.
In any case, I think that if people think really think that they are learning Japanese culture in Aikido class - then they ought to think again.
I have not meant "Japanese culture." I am referring to "budo culture" or perhaps "warrior culture." This is something that many Japanese themselves are interested in today. I find it hard to believe there was a single student of Takeda's for whom this was not their essential motivation.