Approved Document B and the relevant parts of BS5588 (now late and lamented, I guess) specifically prohibit dampers in kitchen (and car park) extract ductwork, requiring fire resisting ductwork should it be necessary to pass through another compartment. As Wee Brian so rightly says, the grease goes a long way, bakes hard, and prevents dampers from operating. And besides, the speed of the flame front is so fast that it would be past the damper before it were able to operate.
Another aspect of kitchen ductwork fires is the quantity of nasty smoke: close a damper, and all of that will be forced back into the kitchen/rest of the building. Many of those restaurant kitchens are airless little rooms in the basement anyway, and I would certainly not wish to deliberately prevent heat/smoke from escaping to the open air, rather forcing it back into the building.
Other threads have highlighted bits of BS9999 that don't seem to be correct, I think this should be added to the list.
And Wee Brian mentions Heathrow: unfortunately, I can come up with a a depressingly long list of other sites totalled by cooking fires..............
Oh, and what makes you think cooking pizzas doesn't produce grease?
