Kompany when he was manager of Burnley in the Championship was totally different from the Burnley in the Premier League. You forgot to add that he was the person to bring them out of the championship to EPL with a marvellous performance. You can't compare that very team to the other teams in the EPL, so I really don't agree with you on the narrative of coaching a relegation team then going on to win the league the next season with another team. Kompany would have still struggled if it was Wolfsburg he was in charge of and not Bayern Munich.
I agree with your view about all point here it's never been easy to manage teams those are having no good sources specially like mentioned Wolfsburg because they are not capable of doing like Bayern Munich, or they are not having depth like Bayern Munich.
Vincent Kompany still can go down if he fails to keep things on balance and Bayern Munich not able to secure wins because he needs to keep eye on always with having good coordination between players and also another important thing needs to be had suitable replacements which give them good performance in case of injuries because many clubs struggle just because of this. Few coaches had good start of their career which surely can help them but still time can keep changing so they needed to have changes into their strategy which allow their players for having better performance.