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.
Yes, I agree with you that if it was Wolfsburg or any average team that Kompany is coaching, and not Bayern Munich, it is very clear that he would definitely struggle and not have a chance of winning the Bundesliga in his first season and even few season to come. This is because Bayern Munich has a different quality of players compared to teams like Wolfsburg and others average teams.
Kompany is a good coach, and nobody can deny that. He has good records before starting to coach Bayern Munich. He was able to promote Burnley from championship to premier despite being the coach who still relegated them. However, the reason why Burnley was relegated was that they didn’t have great players who could withstand the Premier League level of performance. If Burnley had given Kompany money to spend, they could have had a better squad to compete in the Premier League.One of the reasons why Kompany easily won the Bundesliga is because Bayern Munich is already a big club, and that comes with a deep squad of quality players.