Except that it's the ONLY department that actually generates the main stream of income. All other departments are secondary to flight ops. Flights stops, so does your airline.
I know what you are trying to imply by talking "departments" but, Flight Operations is the department that delivers the base product (a seat from point A to point B). Flight Operations Departments are alway a "cost" on a ledger!
If the marketing and sales department cannot deliver enough customers at a price that revenue is greater than the costs your airline will also stop, it will just take a little longer. If your customer service is less that what the customer expects for the price of the seat paid then your airline will wither and die a slow painful death. Every department is co-dependant on the other.
IMHO Having someone with a good marketing background is good for the future of QF because in my experience they are ones that ask the hard questions of "what are we trying to sell" and "what are we trying to be"?
What is QF; "cheap and cheerful JetStar" or "quality full service Qantas". That is the real question that the QF board needs to answer. At the moment they are neither and are being picked off at both ends by the likes of Tiger, Air Asia, Lion at the LCC end by SQ, Emirates, Qatar at the high end.
MBA v Ops Experience
The MBA usually has the ability to analyse and develop the answer to the question but does not know what the question should be!
However the Ops experience knows the question that should be asked but usually does not have the skill to properly analyse or develop the answer.