They didn't fail because they were bad managers - there are plenty of league and CL trophies among two of them, so there was clearly something unique to United that caused them to fail. ETH gets Ajax within a whisker of the CL final then comes to United with massive funds backing him, and pretty much struggles as Mourinho and LvG did.
But they were (relatively speaking, obviously any manager in top leagues is in top 1% of managers worldwide).
Moyes, after failing here, got quickly fired by Sociedad, then relegated Sunderland, then didn't get contract extended for West Ham. He is now doing well, but he needed 8 years between him getting fired and him doing well. And well is quite relative again, no big club would touch him.
LVG after getting fired here, said that he is looking for the right job. But the right job never came, and the only job he got was Holland's manager again, when he bore everyone to death with his brand of football. He also won his UCL 2 decades before joining United, so it is pretty much irrelevant.
Mourinho was unemployed for a year and then best he got was Spurs. He then got sacked by Spurs. And the best he got after that was Roma. He obviously was not a top manager when he was here.
ETH had a very good UCL season when he reached semi. The next season, Ajax couldn't pass the group stage of UCL. The season after that, they couldn't pass the group stage of UCL. The season after that, they passed the group stage but got eliminated by Benfica. So that season looks more like an one-season wonder, rather than him being consistently good in UCL. And let's be fair, many managers got a single good season in UCL, but they were not that great. A couple of years before him, Jardim reached UCL eliminating City in the process. A year after EtH, Nagelsmann reached UCL semis with Red Bull. And last year, Simone Inzaghi reached the finals with Inter (a better funded club than Ajax, but still nowadays not a club that has lots of money and thus not many top players). It happens for an ok, but nothing special manager to have a decent season in UCL, but that well, does not mean much.
I think a better way of judging managers of United is how well they did at United. EtH did relatively well last season, guiding us to third in a season where Chelsea, Liverpool and Spurs were shit. Saying that, we got enough points to end in UCL zone in most seasons. He also won the smallest of Cups. The football for most part was awful, which is always a sign that things are not that well. And the consistent humiliations we got in away matches were a sign of fundamental problems that people pretended they did not exist. The signings looked to have large problems from the beginning (at least to me and another few who do not blindly trust the manager), and this season you need to be blind, and switch off the brain to pretend that the signings were anything except genuinely awful (and no, we do not need to wait for 3 years to confirm it).
So yep, like for the other managers, the less we say about him, the better. He will be a footnote in our history together with our other managers post-SAF, as a mediocre manager (relatively speaking) who failed here, despite spending a fortune in the process.
. So no doubt that he has been backed. If you want to argue whether he has been backed properly, that also don't hold much water because we don't have a DoF or sporting director. The players we signed seems more his signing than the club signing.
) and coach is working with that.