Ray,
You're absolutely right re having to pay to leave a country being crap. Over 130 USD just for the privilege of going on leave or to have a short holiday somewhere and you have to pay this each year!
However, the policy belongs to the country, not the airline. Where the airline is wrong is that they do not extend the "privilege" of assisting pilots to acquire this Multiple Exit Permit to the rest of the staff. Cabin Crew, for example, must apply for a visa each and every time they wish to leave Qatar!
"Control" is the name of the game for Qatar Airway management.
And 'QF' is Qantas. Qatar Airways is 'QR'.