Their argument of using Fire/Thunder/Blizzard absolutely reeks of tradition. And I will show you why:

This list shows the spells which deal direct magical damage, designed to be available to a "Black Mage" in every previous Final Fantasy title. (using most current translated versions for ease of reading).


Final Fantasy
Fire, Fira, Flare
Thunder, Thundara
Blizzard, Blizzara
Final Fantasy III
Fire, Fira, Flare
Thunder, Thundara
Blizzard, Blizzara
Quake
Final Fantasy IV
Fire, Fira, Firaga, Flare, Pyro
Thunder, Thundara, Thundaga
Blizzard, Blizzara, Blizzaga
Quake
Final Fantasy IV: The After Years
Fire?, Fire, Fira
Thunder?, Thunder, Thundara
Blizzard?, Blizzard, Blizzara
Quake
Final Fantasy V
Fire, Fire2, Fire3, Flare
Ice, Ice2, Ice3
Bolt, Bolt2, Bolt3
Final Fantasy IX
Fire, Fira, Firaga, Flare
Thunder, Thundara, Thundaga
Blizzard, Blizzara, Blizzaga
Water

Final Fantasy X
Fire, Fira, Firaga, Flare
Thunder, Thundara, Thundaga
Blizzard, Blizzara, Blizzaga
Water, Watera, Waterga

Final Fantasy X-2
Fire, Fira, Firaga, Flare
Thunder, Thundara, Thundaga
Blizzard, Blizzara, Blizzaga
Water, Watera, Waterga
Final Fantasy XI
Fire, Firaga, Fire II, Firaga II, Fire III, Firaga III, Fire IV, Fire V, Firaja, Flare, Flare II
Thunder, Thundaga, Thunder II, Thundaga II, Thunder III, Thundaga III, Thunder IV, Thunder V, Burst, Burst II
Blizzard, Blizzaga, Blizzard II, Blizzaga II Blizzard III, Blizzaga III, Blizzard IV, Blizzard V Freeze, Freeze II
Aero, Aeroga, Aero II, Aeroga II, Aero III, Aeroga III, Aero IV, Aero V, Aeroja, Tornado, Tornado II
Stone, Stonega, Stone II, Stonega II, Stone III, Stonega III, Stone IV, Stone V, Stoneja, Quake, Quake II
Water, Waterga, Water II, Waterga II, Water III, Waterga III, Water IV, Water V, Waterja, Flood, Flood II

Final Fantasy XII
Fire, Fira, Firaga, Flare
Thunder, Thundara, Thundaga
Blizzard, Blizzara, Blizzaga
Aero, Aeroga
Aqua
Final Fantasy XII: Revenant Wings
Fire, Firaga, Flare
Blizzard
Thunder

Final Fantasy Tactics
Fire, Fira, Firaga, Firaja, Flare
Thunder, Thundara, Thundaga, Thundaja
Blizzard, Blizzara, Blizzaga, Blizzaja

Final Fantasy Tactics Advance
Fire, Fira, Firaga
Thunder, Thundara, Thundaga
Blizzard, Blizzara, Blizzaga

Final Fantasy Tactics A2: Grimoire of the Rift
Fire, Fira, Firaga
Thunder, Thundara, Thundaga
Blizzard, Blizzara, Blizzaga
Final Fantasy Crystal Chronicles: My Life as a King
Fire, Fira, Firaga
Thunder, Thundara, Thundaga
Blizzard, Blizzara, Blizzaga
Final Fantasy Fables: Chocobo's Dungeon
Fire, Firaga, Flare
Thunder, Thundaga
Blizzard, Blizzaga
Quake
Dissidia Final Fantasy
Fira, Firaga, Flare
Thunder, Thundaga, Burst
Blizzard, Blizzaga, Freeze
Water, Waterga, Flood
Aero, Aeroga, Tornado
Stone, Stonega, Quake
Dissidia 012 Final Fantasy
Fira, Firaga, Flare
Thunder, Thundaga, Burst
Blizzard, Blizzaga, Freeze
Water, Waterga, Flood
Aero, Aeroga, Tornado
Stone, Stonega, Quake

Final Fantasy: The 4 Heroes of Light
Fire, Fira, Firaga
Thunder, Thundara, Thundaga
Blizzard, Blizzara, Blizzaga
Quake, Quakra, Quaga
Aero, Aerora, Aeroga
Water, Watera, Waterga
Dark, Darkra, Darkga
Banish, Banishra, Banishga


TL;DR -- Black mage spells are as follows:

Fire-Associated direct-damage spells show up in 18/18 games, with 74 entries. (26.4%)
Thunder-Associated direct-damage spells show up in 18/18 games, with 63 entries. (22.5%)
Blizzard-Associated direct-damage spells show up in 18/18 games, with 63 entries. (22.5%)
Water-Associated direct-damage spells show up in 8/18 games, with 28 entries. (10%)
Stone-Associated direct-damage spells show up in 8/18 games, with 24 entries. (8.6%)
Aero-Associated direct-damage spells show up in 5/18 games, with 22 entries. (7.9%)
Umbral-Associated direct-damage spells show up in 1/18 games, with 3 entries. (1%)
Astral-Associated direct-damage spells show up in 1/18 games, with 3 entries. (1%)