An 80% match fit Kagawa will always start for Japan, because his position is mainly on the left "wing", where his only competition is Inui, who is nowhere near his level. The thing is, Moyes seems to value fitness a lot, maybe even more than SAF ever did. It therefore makes complete sense for him to keep Kagawa out unless he's 100% match fit. You might argue that certain players like RVP or Carrick would start anyways, despite not being 100% fit, and that is probably true. But don't forget that these are players who pretty much carry United. Kagawa, while definitely having the potential to do the same, is just not there yet. He probably will be if he starts playing regularly, but he's not been given that chance yet.
That is why Moyes have chosen to not start Kagawa yet. He's not sure if Kagawa is 100% ready, and seeing as it's still early in the season, risking him wouldn't really make sense. There are many more games to come, not mention the international games he just played. It's better to ease Kagawa into things.
Also, a new manager means a new person to impress. Just because Fergie rated Kagawa, it doesn't mean that he's off the hook now that Moyes has taken over. He has to start over again. And based on what he has done since Moyes took over, it's safe to say that he's not a sure starter. He's a sure starter if we look at his past, but really, Moyes can't afford to do that, unless we're talking about the more obvious choices(RVP and Carrick etc).
The people who think that Kagawa is kept out because he doesn't fit our system or because Moyes doesn't rate him, needs to get a reality check. Or at the very least come back in a few months. If Kagawa still isn't playing then, despite not being injured, then I think we can start asking questions.