If you join two departments on order to reduce personnel numbers then you need a new layer of coordinating management to oversee the new department. This enables you to reduce the numbers of lower level staff while increasing the number of managers.
Parkinson's Law comes to mind in the case of QF. Bureaucracies expand over time, the British Colonial Office had it's greatest number of staff at the time it had the least number of colonies to administer. Therefore QF should have its largest number of managers and administrators at the time it has the lowest number of aircraft and routes.