The problem with Chivu was always obvious and Inter just didn't care at all. The only team he has managed before Inter was Parma and that was only for 13 games.
Before any of that, he was managing youth teams of Inter, which is of course great because that means he knows the team and everyone in it because he both played there for many years, and then still stayed and spent years managing the youngsters there, meaning since 2007, he has been there for a total of 13-14 seasons with them, so obviously that makes it easier for them to hire him since they know him. But getting an inexperienced coach for the job, when you are aiming for a title, was not a good decision. Season is long, we are going to see how he will do.
To me I just see this appointment as a thing of favor and compensation if not that I don't see any reason why they should take him for the job while aiming for greater things in the league and beyond the league, but let's look at it on the other way round if not for the last game that Inter Milan was defeated, I didn't see anything wrong with the team, though the lost was too early and they've got a lot of teams to content with so this lost wasn't really necessary for now, but what has happened has happen let's look forward to what's upfront besides inter Milan got all it takes to still do pretty well in the league.
I don't think Inter Milan management choose to make Chivu their head coach as a thing of favor or compensation because the Serie A is becoming more competitive, and Inter Milan management wouldn't appoint Chivu as their head coach if they know very well he won't perform well at Inter Milan this season. If Inter Milan plays 10 matches this season in Serie A without Chivu gathering a convincing point, Inter Milan management will likely relieve Chivu of his job and hire another coach who can be able to deliver what they want.