This is exactly why I think Kagawa is an important player for us and has been criminally underutilized by Moyes. His movement off the ball to support play is what we need to unlock teams and is a step forward in abandoning the rigid formation which saw us produce tumescent football time and time again in our side.
And this is in my opinion a very important issue about the situation of Kagawa and english Football in general.
People look at the obvious, at what a player brings directly into the game and a lot less at other aspects.
Sure, there are players individually way better than Kagawa, but Kagawa brings something to the table, which you can't measure. Intelligent movement. If he pushes a player in a narrow situation where he then loses the ball, it can't be measured. If he runs a smart way to pull out a defender so the teammate can run into the gap and score, it can't be measured.
Kagawa is not a player who makes the team individually better. He is a player who makes the team as a whole better. This is why he was shining so much in Dortmund where the team worked as a whole. And this is also why he had strong issues so far under Moyes, when the team didn't work properly as a unit.
Surely Kagawa has to improve as an individual player nonetheless, but if Moyes is lacking the ability to see what he brings to the table, then he isn't worth being a coach of a big club.
That also is a general problem about english Football. There is too much focus on the individual player instead of the team as a whole. That is why Real Madrid was so long unable to perform in the Champions League. That is why Chelsea could win a lot of national titles, but only when they worked as a unit they won the Champions League. That is why Athletico Madrid and Borussia Dortmund can keep up in their leagues.
And that is also why Manchester was yesterday able to compete with Bayern. When a team doesn't solely focus anymore about being the sum of its players, but instead of being a unit, they will get stronger in the direct competition (over the duration of a season naturally the individual players can and will win games, especially against weaker teams.)
An interesting article about this topic about the NBA player Shane Battier:
http://www.nytimes.com/2009/02/15/magazine/15Battier-t.html