It isn't about Inzaghi being done with Brozovic. It's about Inzaghi considering Mkhi irreplaceable in our starting lineup. He's the only midfielder who never gets benched. Never. Hakan has got rested. Barella has got rested. But Mkhi always plays. Last time he was benched was in the meaningless game against Bayern in Munich where we mostly played with bench warmers (Asllani, Bellanova, Gagliardini, Gosens, Correa, De Vrij). Since then Mkhi always starts, whether it is Serie A, SuperCoppa, Coppa Italia or CL.
So you have Mkhi who always starts. Then you have Barella who's considered a starter and there's no one else in the squad who can play his role. So it's between Hakan and Brozovic for regista role. It's hardly surprising Inzaghi chooses Hakan who has been in great form all season rather than the guy who just returned from a long term injury.