Tldr; Kagawa and Mkhi failed on equal parts due to us and them, mainly due to tactical differences between where they played and what we played, there is no Dortmund curse.
The issue here obviously stems from the fact we've bought 2 players from Dortmund now in Shinji Kagawa and Mkhitaryan and both have failed to live up to the promise they showed at Dortmund. But I don't believe it's as simple as it sounds, I would say they both failed for different reasons, but there is a correlation to a degree that they both failed here after coming from Dortmund, i'd like to explain why I think this is, coming from a tactical perspective.
Now with Kagawa i thought he showed flashes of brilliance with us, it's unfortunate that i'd find he'd play pretty well and almost never got the opportunity to carry on a streak of games and get his performances up, although his injury early on didn't help with this regard, but our usage of him was completely incorrect from the get go. Now as we know at the time Dortmund were a fast paced, one touch attacking team with lightning transitions, Kagawa was virtually the #10 or support striker who was given a hell of a lot of freedom in a positional sense because of their pressing and counter attacks, there was a lot of off the ball movement and in a pivotal sense this was great for Kagawa because he could play through all of this. However, for us he was mainly used as a left winger in a system that never used inverted wingers, with mainly slow passing, we played absolutely nothing like Dortmund, instead it was mainly touch and get into the box for a cross, particularly under Moyes, we played completely against Kagawa's strengths, in actual fact i've no idea why we even bought him if the idea was to play him on the left wing, he was never a winger, not blessed with lightning pace or any attributes usually thought of in a United winger, I loved the little guy but the transfer really didn't make sense unless we were going to switch a formation that had high emphasis on a #10/CAM instead of the general 4-4-2. This coupled with a higher physicality meant that Kagawa didn't have much of I chance, i think.
I mean there's a video on YouTube with a rather... hyperbolic and stupid name admittedly, but it clearly shows how many times our players ignored a simple forward pass to Kagawa to keep everything going and moving forward only to opt for a safe sidewards or backwards pass instead, or a hopeful lob into the box.. Case of round hole, square peg. I personally think had Mourinho come in after Ferguson we'd of got a lot more out of Kagawa and he wouldn't of gone.
Mkhitaryan is maybe a simpler case, and failed for two reasons, mentally I believe he couldn't handle Mourinho's style of man management, and secondly he was also misused in a way similar to Kagawa, I remember reading a recent article about similarities between Bergkamp's time at Inter and Mkhitaryan's time with us, Bergkamp went from Ajax to Inter and was awful, even contemplating retirement before he went to Arsenal and flourished, because he was a player that had all his qualities negated by Inter's defensive style of play as opposed to Ajax and Arsenal's attacking one.
I mean we all say here that it looks like, upfront, we lack any real coaching and that Mourinho pretty much leaves our attackers to do what they want, individual brilliance, it's been commented that he's done this at previous clubs as well, which is why we often look lost or lack that final pass and such, and this is a huge part to why Mkhitaryan has failed as well, we only have to look at Mkhitaryan over the past few seasons to know this, under Klopp he did okay, nothing special, but under Tuchel is where he came alive, and the reason for that is because of how Tuchel sets his team out as a manager, his attacking coaching is almost second to none and he runs his teams through attacking scenarios, drills, you name it, he may be a little naive defensively but this is why Mkhitaryan flourished, it is because he and his team mates around him had perfectly executed attacking scenarios to play through, he is a collaborator, and we don't play this way, again, we play the opposite of this with seemingly no attacking coaching at all, or at least, very minimal. Flashes of brilliance again, yes, but nothing more.
Now of course people will say it's excuses or semantics, they should adapt and such, but these players only reached the level they did because of the system they were playing in, take them out of that system, don't play to their strengths, and it should be of no surprise they don't play to the best of their ability, again see Bergkamp at Inter, one of the best players in the world but at Inter he was awful and he explains why himself.
Now as for Weigl, well we can only speculate on if the same thing would happen again, but he's a very different player to both Kagawa and Mkhitaryan, we've ran with a system that can accommodate a Michael Carrick for years, and this is what he is, pretty much as close to Carrick as you can get... personally? I'd say it's worth the risk and i'd love to see him here, I don't believe in this Dortmund curse, you buy the players that fit your system, you shouldn't try to force players that aren't a great fit into your system and wonder why they don't work.