Mandzukic's role is not just to get a match winning goal. He gives a lot tactically. If you want to go to the biggest simplification: Mandzukic is a giant expert in aerial duels. He opens up that route to get the ball forward. Kick it to front-left and there is a great chance that Mandzu will win the duel and lay the second ball to Alex or Ronaldo. This can be great, it can serve to release pressure, to apply pressure, and to start moves. A quick look at stats I see he won 5! aerial dules in those 60 minutes, he won 4/4 in the offensive phase, as well as 2 tackles. Yes he is out of form but he gives something different that Allegri is trying to get.
Playing Kean might turn out great, but lets understand why Allegri is playing Mandzukic.