Why do firefighters recommend the use of a deluging volume of water when extinguishing an oxidizer-supported fire?

I'm not a firefighter nor do I have any of their training but I would guess that an oxidizer-supported fire

a. is hotter than other fires.
b. can easily ignite again after being extinguished.
c. therefore, the cure is to heap lots of water on it and keep it (the water) going until the central part and the periphery of the blaze has been cooled below the re-ignition point.