As my post explained, different players fit in different systems, this is part and parcel the issue with not having a DoF, the need to identify a player that fits in with the system the club has been deploying for a consistent period of time.
Kagawa was a #10/SS in a quick, pressing, fast passing, positional Dortmund team, most things went through him. At United he played left wing in a more rigid 4-4-2 that didn't use inverted wingers. We should never have bought him unless we were going to switch to a different formation that relied more heavily on a #10, and people wonder why he failed.
Mkhitaryan is a collective kind of player, a collaborator with teammates, no coincidence his best ever season came under Tuchel who meticulously plans out and drills into players attacking scenarios and options, Mkhi had players all around him and they executed those plans to perfection. We've all discussed how this team looks completely barren on the attacking coaching front, Mourinho relies more on individual brilliance, Mkhi showed some of it, but again he was bought on the back of his great season because of his numbers with clearly no thought as to how and why he was able to achieve those high number of goals and assists.
For the record i think Kagawa would of done a whole lot better under Mourinho than Mkhi, and particular better than under Fergie, Moyes and Van Gaal. It's simply not a case of every Dortmund player who leaves will fail, you need to look at each individual case and why they failed exactly.
Weigl is a bit different in that I think he controls the system, he has the keys to Dortmunds system, he is in affect a DLP, call him a Carrick, a Xabi Alonso if you will, I believe he can fit into any system because he's a controller of the game and would be a perfect buy for us, but I believe he will probably stay with Dortmund next season although i'd love to see him here.