Yeah, Red Mages get Mirror Image which is a huge benefit for Fighter/Mages.
They also get Enlarge, which is my favourite buffing spell, giving Giant (23 IIRC) STR for many hours at high levels. So with only White Mages you'll miss that, not to mention Haste which is the ultimate buffing spell.
My white mages have enlarge and haste
I checked the Dragonlance Adventures hardcover rulebook, and each order of mages is restricted from a few schools of magic:
White: Alteration, Illusion, Necromancy, Phantasm, Summoning
Red: Abjuration, Charm, Enchantment, Necromancy
Black: Abjuration, Alteration, Conjuration, Evocation
Note that the Players Handbook lists spells as belong to Charm/Enchantment, Conjuration/Summoning, and Illusion/Phantasm but never just one of these separately, and even the Spell Summary section near the end of Dragonlance Adventures still lists these pairs together, so it isn't entirely clear which spells are allowed to white mages being able to use conjuration spells but not summoning spells or to black mages being able to use summoning spells but not conjuration spells.
Enlarge and haste are both alteration spells and therefore should not be usable by white robe wizards or black robe wizards.