In certain cases the planes have already been paid off,
They may have been "paid off" but until the cost of buying them is recovered, they're still and expense.
For example, I may have spent 6,000 on a car that I use for work, but until I've had that car make 6,000 for me(exclusive of operating costs), I still haven't "made money" on the car. That's why you have depreciation. The cost of obtaining the asset (car, airplane, piece of equipment) is depreciated over a period of time, as an operating expense, so that at the end of that period of time, it's "book value" is 0 dollars. THAT's when any money made by that airplane starts being "clean" (exclusive of operating costs, etc.).