From what I recall guys like Modric started off as a Kagawa type player, being played on the wing or VERY far fowards in midfield, have since been dropped deeper and now plays for Real in that position.
Football is in 99% of games won and lost in central midfield. Carrick is awful, he offers exactly nothing defensively so Kagawa would do no worse there, likely better as good attacking players have great positioning and reading of the game which helps defensively. Offensively he can't help but be a ridiculously massive improvement on Carrick. Someone who can control the ball and pick out the right pass rather than move it in 5-10 yards in any direction with no thought about counter attacking, creativity, vision or winning the game.
Lampard has been exceptional when asked to drop deeper for Chelsea, as have many of the best most attacking players in the world. Pirlo hardly looked crap when getting deeper and deeper.
I'd take Kagawa over Carrick in central midfield every single time. He might not be the best player to put in central midfield, and it may waste some of his attacking talent, but he's still a massive step up from Carrick. Most truly great players are pretty adaptable and won't suck just because you change their position.
Also...... lol. 1-0