Dybala and Berna dont really have there strenghts in countering either. Sure they can do it better than Mandzu and Higuain, but they are still better in a possesion based team IMO.
The thing is we have the players to play a game focused on possesion. Marchisio, Bentancur, Berna and Pjanic are all players, who are good on the ball. Allegri just chooses brainless runners like Matuidi, Khedira and Sturaro instead of them.
I have to agree that Allegri coaching style is better suited for a counterattacking team. He could not get the team to play a cohesive attacking brand of football if it would save hes life.