Why should I update fighter war room?

It gives you building power and an edge when your APC is filled with the same kind of troop (i.e. all fighters). But the one reason that led me to start upgrading is that Fighter War Room level 25 is pre-requisite for 5 strategic buildings: combat readiness room, communications interference tower and 3 special training centers (fighter, shooter and vehicles). So do not neglect especially the Fighter War Room. It gets really costly but it’s worthy it.

The fighter war room (and the other 2 war room buildings) give buffs to your attacking APC's when you only have that type of troops in it. So if you place all fighters in the formation. When you get to a higher level and are attacking high level players for kill events and duels this can be a good advantage to have. It is perhaps less needed when you are at a lower level.

The other benefit though is that the upgrades give good power increases which can be very useful when getting points of building events in daily challenges and Clash of Zones.