The squad was aging that's true, but Allegri still got his wish and signed over the hill Mark Van Bommel to add to the misery. And the younger and more talented Pirlo couldn't get a game and eventually left for Juve.The team he inherited was ancient, with the likes of Filippo Inzaghi , Flavio Roma , Mario Yepes , Alessandro Nesta , Clarence Seedorf , Massimo Oddo, Nicola Legrottaglie, Gianluca Zambrotta, Mark van Bommel, Marek Jankulovski, Massimo Ambrosini, Christian Abbiati, Gennaro Gattuso, Kakhaber Kaladze and Andrea Pirlo all in 30+. Then you had Ronaldinho who was as good as retired and rumours were circling around Thiago Silva leaving. There's a very valid reason why Ancelotti left the circus. It was evident were AC Milan were heading to and he refused to be dragged by them into the pits.
Allegri had to rely heavily on a team made up largely made up of ancient players who won it all and were therefore difficult to motivate and players who a nightmare to manage such as Ronaldinho, Ibra, Robinho, Cassano and Pato (who was screwing Berlusconi's daughter). Most manager would be frightened by it. He won the league with them.
I am not saying that Allegri is the solution to our problems. All I am saying is that unlike our previous managers or any milk sop/flavour of the season, Allegri is quite experienced in managing a squad which is far from perfect and still punch above its weight. He did that with Cagliari, Sassuolo, Milan and to a lesser extent Juve.
Ibra, Cassano, Aquilani and Robinho were signed with Allegri's blessing because he was the man at the helm when they were signed.
Pato scored 14 league goals in the scudetto winning season which was the joint highest along with Ibra and Robinho. The affair with Barbara had a very positive effect it seems.
He won the league because he had the best CB in Thiago Silva and the very experienced Nesta alongside him. Pato, Robinho and Ibra were also very good and all 3 players scored 14 goals each in the league alone that season. The midfield was Seedorf, Van Bommel and Gattuso. The challengers were Inter at the time and they were also a aging team. Basically the league was very weak at the time which helped, and the aging squad argument doesn't help Allegri, when he himself added a past it Van Bommel and was competing against a aging Inter.