Adding more administration to reduce the number of management seems like a good trade, simply because management-days cost more than administrator-days. If 7 managers are each spending one day on a task that would be done twice as quickly by an administrator paid half as much, you're trading 7 manager-days for 1.75 manager-days completely disregarding the cost of manager context-switching.

And if you're that administrator, you probably don't need to justify your purpose, you should probably ask for a raise.

I'm not sure where else economies of scale are supposed to come from.