As some comparison was made to vessels, I can offer the following.
I've served on two classes of Australian Submarines, and on both classes, when we conduct emergency casualty drills with the 'bomb chuckers' on board, galley fires were up there with the drills, probably only running a close second to engine room fires.
Heating in the galley, oven, grills etc were provided by electrical current. On both the Oberons and Collins, an isolation switch was provided just outside the galley, in the event of any fire, the galley circuits, 440VDC, 220VDC and 115VAC would be isolated. Removing the energy source is an excellent first step into overhauling a fire.
The Oberons also had a 'deep fat fryer', (DFF) of course with oil (perhaps the Poms actually did use lard or dripping in theirs). I think 90% of the fire scenario's we had to deal with on the Oberons were in the DFF. In addition to removing the energy source, the DFF also had a spring loaded flap over the top on a detent. It could be tripped from within and immediately outside the galley.
Along came Collins subs and it was decided the galley did not need a DFF, mainly for health reasons, but also further eliminating a potential fire risk. Although some fitter and turners would take a bench top DFF with them on deployment, would operate ok on 60Hz as it's only a resistive load.
The stoves were another source of fires, the insulation was prone to at least smouldering, if not catching on fire if fat, oil or grease wasn't contained and got a chance to soak into the insulation.
Generally an AFFF (Aqueous Fire Fighting Foam) or gas-water extinguishers were not permitted to directly attack a fire in the galley, they could be used for boundary cooling or as last resort. Preferred extinguishing medium is dry powder, BCF or Halon 1301.
Slightly divergent to dining cars, Relay Vans as introduced by the SAR and then adopted by the CR started out with wood fueled stoves. Wood fueled stoves later progressed to gas, along with gas absorption refrigerators. Relay vans now are all electric. The stove tops don't have fiddles, but do have a surrounding barrier, which at least contains pots and pans generally on top of the stove.
I'd personally still like to have a gas stove in the relay vans, I hate cooking with electricity.