Leipzig and Gladbach are fairly structured clubs with a clear philosophy: for example everyone can probably describe the typical Leipzig player: young, talented, but also a decent athlete/worker. It's a mindset and recruitment strategy that is implemented and maintained from the top of the club, regardless of who is currently coaching. Gladbach don't have the money to sign as many highly regarded talents and they don't have the feeder clubs to test drive the more obscure youngsters, but they have a very powerful DoF in Eberl who maintains their identity.
I mention this, because while these teams may only offer Rose and Nagelsmann limited ressources compared to what they hope to achieve their squads are actually built cohesively to accommodate a modern coach like them. United's squad is more patchwork, which could easily become an issue if someone does not fit with some of their fundamental ideas of how they want their team to play, but can't just be axed. Nagelsmann in particular seems to be planning his career quite carefully, I obviously don't know how he feels personally, but I wouldn't be surprised if he'd just turn down United, because the risk of getting burned is too high.