Racial modifiers are related when it comes to weapons and armors.
Demons are simply renamed Insects/Reptiles (whatever they decided to call them in each incarnation of FF4).
It's easy to verify when you compare the monsters that have those racial modifiers. They are more or less the same (assuming you are directly comparing FF4 PSP vs FF4A/FF4).
The reason why there IS a new weapon (for FF4:TAY) is because you have to look at the overall scheme of things when it comes to that racial type.
I'm not sure of the TAY data (since noone has looked into it in depth), but the only base FF4 equipment that dealt with this race is the Ice Shield AND the Ice Rod. You would never know this by the weapon description.
Also, think about the application of the racial distribution as it relates to armor in classic FF4.
Undead - Crystal armor set, Ragnarok, "Paladin" armor set, Holy arrows - mostly useful for Mt. Ordeals
Ghouls - Silver/Mythril armor set (including the Silver Ring) - too few monsters use this designation when you can BUY the Silver/Mythril armor set
Mechs - all Hammers (which Cid never gets to smash with), Maxmilian (FF4A, only armor), Thunder Claw, Lightning Arrows - bad situations with either Cid equipment
Flan - Blood Lance/Sword, Flandango (FF4A only) - no armor for this set until the TAY version (Ancient Sword is better than your options since it is accessible earlier)
Giants - Charm/Fairy Arrows, Ogre/Poison Axe, Charm/Fairy Claw, Giant Gloves - plenty of weapons, resistance requires a rare drop
Dragon - Dragon armor set, Wyvern Lance, Dragon's Whisker, Artemis Arrows, Gold Hairpin, Crystal Ring (rare drop) - hard to not find a dragon in the Lunar Subterrane
Mage - Rune Ring, Mage Masher, Elven Bow, Silence Arrows, Rune Staff (rare), Aegis Shield - there's plenty of mages to deal with when you get all of this stuff
Reptile - Ice Rod, Ice Shield - Ice Rod barely used for physical attacks on the Turtle, Basilisk, Gargoyle... Ice Shield used against the Black Lizard and Lamia... that's about it
So, when you look at it, the Demonsbane only corrects the fact that there isn't a viable weapon to take care of that racial modifier.