I'd like to know why you think that. To me, I'd only see this as a problem if we don't have someone like Mata or Herrera in midfield who look for the ball and dictate play from midfield (if we aren't playing a counterattacking setup) or if we play players who are poor with their movements.
First of all i did not get your point about Mata, Ander. If Mata will look for the ball and "dictate play from midfield" what will Kagawa do in this number 8 role? Sideway passes all around? No thanks. It's number 8's job to dictate the play, while team with the ball, Mata's job should be then to actually create chances and be in the box, finish them as well.
I think Kagawa can't really be a good number 8 in PL mainly due to his lack of strength. With the ball, in attack he does not possess good enough ball protection skills, he looses ball far to easily esp. when physical pressure is applied, and you know you can bet your house that it will be the case in Prem. You probably could get waay with it in Spain, maybe in Italy, but in England you need a certain grit to shrug off challenges. Then without the ball to apply the said pressure yourself, to tackles, to win ball back. Kagawa is a bit of a pushover in that respect. And i don't think you can make do with only one strong player in the middle.
I mean you could probably do with a 1 DM, 2 CM triangle, like a just for example sake
Fletcher
Kagawa-Vidal
Where Kagawa has one defensive player to cover and one ball winner, more of a b2b player. But that's a different formation and in Kagawa will have more of a number 10 role in that system.
So for me Kagawa in number 8's role can work only as a sort of emergency option, when opposition is in "bus mode", when their CM players do not even want to think about crossing halfway line.