Kompany helped Bayern Munich get improve however he is not the first choice for this team and they were about to hire some other coaches instead of Kompany. As far as I saw in the news the management of Bayern Munich asked Pep Guardiola and he advised them to hire Kompany and you saw so far Pep was not wrong about this coach in Bayern Munich but still even his good performance doesn't mean he can win the title on Bundesliga with Bayern Munich but still Leverkusen is very close to them and if Kompany and his player make any mistake, Xabi Alonso is there to take their place.
When Kompany was handed the charge at Bayern Munich, the management should have thought whether this manager would be able to carry out the duties of Bayern Munich properly. If he is given the responsibility now in the middle of the season, if he is removed and someone else is given the responsibility of the club, it will certainly be a blow to the reputation of this manager.
I see no reason why Kompany should be fired, he should be given much time, that shouldn't even be on the table for now for any reason. He is doing well in the Bundesliga as far as I'm concerned, Bayer is only at a gap closer because it is good, and in spite of that, Bayern is still leading with a good 4 points and I don't think another coach would have done better. If it is to win the UCL, the club should not be too desperate, they've not won it in a decade and Kompany will not do a magic in less than a year. Still, his team should have done better against Feyenoord, as the 3-0 in UCL shows Bayern's weakness against an external league.