For the past 47 years I have managed cruise ship hotels. During that time period I have personally witnessed / been involved with around 50 cases where passengers and/or crew suffered serious burns from Baked Alaska parades, tableside cooking, etc. I could probably find another 50 “old timers” with similar numbers. We might come up with 2500 or so cases where there were serious injuries over the past 50 years. This is not “countless numbers”, but it is a significant number of injuries that should not have occurred and could be prevented.
Fires started by careless smokers happen far less often. Serious injuries from those careless smokers are even more rare.
The great majority of ship fires occur in the trash incinerator, the laundry, the galley, and the engine room. These fires almost never result in serious injury.
If I were a cruise company lawyer, I would most likely focus on fire events that cause personal injury and lead to costly lawsuits.
Those would be the Baked Alaska and tableside cooking events.