The coach has to do a few things:
1. Have some tactical knowledge, being able to adapt and try and counter the opposition
2. Motivate the players, put pressure on them to fight for their spot in the team
3. Help develop the players and squad tactically, young players are a club investment so it's in the best interest to help them grow
You can do all the above but not win trophies, but if you do the above then you'll one day would have built a team to challenge for trophies. This is how the top clubs scout their managers - they look for these traits.
Gasperini and Inzaghi have these traits but you'd still think they'd fail at the highest level, we can't be certain but I'd not judge them until I saw them with us.
Now, since we find Allegri and Zidane available, they have the 3 main characteristics plus they have an already great trophy haul. It's not even a debate what we should do. If we screw up this moment then go Inzaghi and back him, no more wannabe hero chess moves from the management.