There probably isn't much point in firing the engine fire extinguishers if you are evacuating because of a fire in the toilet!
Pulling the fire handles makes sense as these bits of kit do a lot more than most realise.
On the B777, when the Engine Fire Switches (still look like handles to me!) are in the normal position they are mechanically locked in place until
either an associated engine fire warning
or an associated Fuel Control Switch is set to cutoff. (A Fuel Control Switch at cutoff also ensures the passenger door flight locks are unlocked.)
(There is also an override switch that unlocks the Engine Fire Switches if you wish to use it without the above 2 conditions.)
Once pulled, the Engine Fire Switch:
arms the engine extinguishers
closes the engine and spar fuel valves
closes the engine bleed valves
trips the generator
shuts off the hydraulic fluid and depressurises the hydraulic pump
removes power to the thrust lever isolation valve