Just in the last three years (some multiples), I have left from: Lisbon, Istanbul, Paris, Bordeaux, London, Moscow, Shannon and lastly Florence (just this week). I have never had to pay a departure fee or tax.
Are you maybe seeing a separate charge of several hundred dollars during the booking process? One that maybe is described as air taxes or fees? Something that can be broken down as possibly looking like:
airfare $ xxxx
taxes $ xxx
hotel $ xxxx
Airfare and taxes are inseparable during the flight booking process - both have to be paid at the same time and show the full price of the air tickets. They are often listed as separate charges though. They are always paid upfront. Does this clarify things for you?