So I actually did my research once again. Listing games with defined job system.
Final Fantasy I Black Magic:
http://finalfantasy.wikia.com/wiki/M...29#Black_Magic (Quake is here, but it's techinically an instant kill move, non-elemental)
Final Fantasy III Black Magic:
http://finalfantasy.wikia.com/wiki/C...II_Black_Magic (FTI + Quake now a proper earth elemental spells)
Final Fantasy V Black Magic
http://finalfantasy.wikia.com/wiki/C..._V_Black_Magic (Fire, Thunder, Ice onry)
Final Fantasy Tactics Black Mage , Final Fantasy Tactics Advance Black Mage, Final Fantasy Tactics A2 Black Mage
http://finalfantasy.wikia.com/wiki/B..._%28Tactics%29
http://finalfantasy.wikia.com/wiki/B...ics_Advance%29
http://finalfantasy.wikia.com/wiki/B...8Tactics_A2%29
(Fire, Thunder, Ice onry)
And now games without a defined job system
Final Fantasy II Black Magic:
http://finalfantasy.wikia.com/wiki/C...II_Black_Magic (Fire, Thunder, Ice onry)
FFIV: Palom and Porom do learn Quake as black magic.
FFVII. FFVIII: Has no "black magic" definition
FFIX: Party black mage learns Fire, thunder, ice and one water spell
FFX: Fire, Ice, Water and Thunder are Black magic
FFXI+: Entire elemental wheel is considered black magic
You miiight have a bit of a point with quake since it was on I and III, but not the full elemental wheel. FFXI is the only job system FF game in which black mage has access to all elements. Only after XI that games really started considering all elemental magic as black magic
I gotta leave work, else I'd actually check black mage movesets in the chocobo spin off games.