fire mage cannot use ignite and rain of cinder infinitely. Hold on to dragon hatchling, higher stat or support cards until the spells are used while using lower stat cards to kill his minions, most of it's minions die after dealing damage. Hold onto a few cards to prevent out of card damage
One damage is enough to one-shot most summons since most summons HAVE one HP. Furthermore, the fire mage "occasionally" gets 'Ignite' cards that deal 5 damage. And by occasionally, I mean he gets them whenever you place down high-HP summons.
And a "two turn insta kill" doesn't mean much in the scheme that it either guns down anything that gets close as well as having summons on top of that.