I often see people comparing Kagawa to other attacking midfielders who perform well on the wing, and use this as an argument against Kagawa. I think it's important for these people to understand that Kagawa started his career as a deeplying central midfielder. He was only moved further up the pitch because his coach in Japan felt that he had too much attacking qualities to just control the game in midfield. I'm pretty damn sure that players like Silva, Mata, Özil etc didn't start their careers as deeplying midfielders. That makes Kagawa a bit different to these players, and it's therefore pointless to expect him to adapt the same way.
Yes, Kagawa plays on the left for Japan, but that's a totally different style. Their fullbacks are extremely attacking-minded, and are expected to have full responsibility over the width. That is why Japan occassionally changes to a 3-4-3 formation. The 3 players who are playing behind the main striker in the 4-2-3-1 formation, have usually been the following: Kagawa, Honda, and Okazaki. That's 2 attacking midfielders who have spent the majortiy of their careers centrally on the field, and a striker whos style has been compared to Michael Owen. With this information in mind, do you think that Japan sounds like a team that plays with wingers? No. Japan's formation is extremely narrow and interchanging. There's no room for wingers.
Using the Japanese national team as an argument for playing Kagawa as a winger is therefore incredibly stupid. Not only because their style is completely different to ours, but also because the opponents Japan face on a regular basis aren't nearly as strong as the opponents we face. And to top it off, Kagawa is actually not that good for Japan. He's good, yes, but compared to his Dortmund spell, he's a joke. That's why Klopp's heart is broken seeing Kagawa play on the wing for us. For Japan, it's no biggie. It can't be helped, given the set of players that they have and the style that they use. But for United, it's a waste.
Does this mean that Kagawa can't be a success on the wing? No. He can definitely become a success. But will he ever become World Class? No. Will he ever become so good that he's irreplaceable? No. Will he play the same important part for us that Silva has played for City? No.
People need to keep that all this in mind. As an AM, Kagawa has the potential to surpass all these flashy AMs(Özil, Mata, Silva, Iniesta etc). That's how good he is. But as a winger, he'll become a good player at the very best. If you're OK with the latter, fine. Play him on the wing. I can stand behind that, because I still think he brings something good to our team, even on the wing. But it's still a very bad call in the long run.