I can't speak for every single fitting room in Japan, just the ones I've tried. Since clothes here aren't exactly made for my foreign body, I am not exactly the most experienced person in this regard. That being said, I can say that at least some of them require you to remove your shoes before entering them. In fact, that is the way in which you indicate the room is occupied in some cases. If you see a pair of shoes outside, someone is in there. Considering that some of them are covered with nothing more than curtains (as is also the case back home at times, or so I'm told), I guess this is better than nothing at stopping people from barging in on your partially naked form.
Taking your shoes off and putting them back on just adds one more step to the cumbersome task of trying on clothes and I won't miss it when going into a Japanese fitting room.