First of all, Inter without Inzaghi can become a different team, the same goes for Milan with Alegre, and maybe even Fiorentina with Pioli (although I'm not so sure about that). After Juventus lost its dominance in Serie A, this champion has become very changeable, the leaders are constantly changing, and it's difficult to predict anything, by the way, Napoli have never been famous for great stability over the seasons, and they will have to play in the Champions League, which can affect their results in Serie A.
Inter Milan won Scudetto with Conte and Inzaghi took over the head coach position from Conte in doubt too. However, Inzaghi actually had experience as a head coach in Lazio and he managed Lazio successfully before moving to Inter Milan. How he was appointed as Inter Milan head coach is very differently than how Chivu was appointed to this position weeks ago.
Inter Milan won Scudetto with Inzaghi and performed well in Champions League too, so it makes a lot of pressure and expectation on Chivu. While we know that Chivu is purely a young coach and the coming season will be a first time ever he manages a club at a head coach position. This new season will be very challengin for both Inter Milan and Chivu with very high risk of failure.