I'm tempted to say whatever happens next won't even make a difference. If we continue with Inzaghi, which I think we will (at least for still a handful of games), we obviously will continue to suck. There seems to be a deep rift between the players and the coach. Inzaghi himself seems to be completely out of ideas and those substitutions today were quite simply bizarre. If we don't turn the ship around asap, which at the moment looks rather unlikely, a top 4 finish is in serious jeopardy.
If we indeed go ahead to sack Inzaghi and appoint a new head coach, I 100% guarantee you that it's going to be someone that absolutely fucking nobody wants to see here. Whoever comes next in this hypothetical scenario is bound to flop.
It's not even about the coach at this point. I've said it before and I'll say it again, the squad just not that good. Yeah okay, we have a few great players, who used to be good until last season, but a lot of the squad is composed of players who were very mediocre at their previous clubs before they came to us like Acerbi, Correa, Hakan, Mkhi, Dzeko etc., who now start every week. Gosens almost never plays, Dimarco and Damian are painfully mediocre. The bench is just a burning dumpster as a whole. That leaves us with a bunch of players, which could do more, but at the moment simply don't.
Long story short: The club's fucked for the foreseeable future. The team either needs excellent scouting or an insane amount of investment to become competitive again, both of which is unlikely.