Since this is actually a Cataphracts in Iron thread, I was waiting to see if a new thread would open for this topic. IMO, the purpose of the fire galley is two-fold.
1. It comes out of the dock quickly, making it very good for combatting people destroying your dockblock with hand to hand troops. They will fill the void in front of the dock, which is also helpful. They will bite it badly against missiles, though.
2. It is incredibly useful for destroying transports. It outruns them, while the others ('cept Greek) simply pace them. A couple FGs is a very cost-effective way to deal with those invasion fleets of Cents and HCs. (Those 200 HP go down much faster, easier and safer than the 1500 or more HP that are about to land.) And if they are one of those unfortunate civs that only get light trannys, hope they swim well in armor.
Keep your stick on the ice.