@Proxima,
By its very nature, each department will see their own mission as top priority. If each department is seen as equal to every other department, how will one department be forced to concede resources to another in case the need arises?
Departments will no doubt still compete against each other for priority of command as well as monetary and other resources. Instead of financial gains, these conflicts will basically become fuel rods for the department head's egos.
Once again, the average citizen will suffer the consequences as departments will battle over who is in charge of crisis X and whose department is forced to do the unwanted dirty work as well.