They stick with short-passing and intricate movement because that is how Nasri, Silva, Aguero and Tevez wanted to play.
Even when Dzeko was playing those players were still on the pitch so you don't start hitting long passes and cutting out Silva etc completely.
You build your team to play the way that the majority of your players want to play/are best suited.
Stoke, full of tall and strong players. Play long ball.
rags, full of fast wingers and a slow midfield so cut out the midfield and hit the wingers every time to get the ball in the box.
Arsenal, have players who want to play short passes and tiki taka and so on. They play that way. They have Walcott who would strive on the same passes as the ones Dzeko apparently needs but they don't stick him up top and hit passes all day they play the same passing game as us because thats what Arteta, Wilshere and Cazorla etc want to do.