Kompany does not have much experience as a coach, his limited experience and having never handled a big team has made many people doubt his ability to handle Bayern Munich. After ending the season without winning any titles with Tuchel, Bayern Munich officials will have high hopes for Kompany to improve the quality of the team next season. It is not easy to coach a big team like Bayern Munich, the coach will always be required to be able to present a title at the end of the season, if the coach cannot win any title, then he will be considered a failure and unable to manage the team.
I think this is one of the toughest tasks for Kompany as a coach. Burnley was a relegated team this season and it was not a good report that allowed Kompany to coach Munich. I don't know what the club management is thinking. I don't think Kompany is that bad. As far as I remember, he was trained by Guardiola and maybe he can apply Guardiola's tactical philosophy to the Munich squad. Burnley is not a big team in the English league so if they are relegated it is possible that it is because of poor coaching or because they do not have a decent squad. I think the Munich club board is considering the second option so Kompany is on their list.
Yes you are right, Kompany will have to prove himself because chosing to become the manager of a big team like Bayern Munich already shows how ready he is willing to improve his technical abilities because Bayern Munich has already witnessed his performance as the Burnley head coach and saw how the team was relegetd last season,I believe here must be something the Bayern Munich management saw in the portfolio of Kompany before giving him the job as the head coach of the team so he's going to do his best together with the players in the team to make sure the team gets better than last season.
The experience that Kompany has gotten under the management of PEP Guardiola is also going to help him work with the Bayern Munich team so adding his experience together with the people he's going to work with will sure help him to win trophies for the team which is the reason why the club appointed him as the manager.