As she says in one of the seasonal armor pieces,
“Ghaul commanded you to die for his vanity. I ask only that you fight at my side for the empire. The choice is yours.” —Empress Caiatl
I feel that Caitatl doesn’t respect her father as much as she does or did Ghaul. After all, like @LordSaladPan stated, Xivu Arath was going to come whether the Cabal had a military leader or a more relaxed one. After all she was driven to spread the darkness in their hunt for the Traveler, and Torobatl would have been basically a stop on the way to Sol. Whether the inhabitants wanted Xivu Arath to arrive or not was not a determining factor.
Therefore a more military approach would have been a better defense against the Hive.
And in response to @baxter, I believed Caiatl saw her own father as “lazy and incompentent”, and Ghaul as a stronger figure for power. This is probably why she overthrew her father in the first place.