Historically red mage wore heavier armor similar to what the Dragoon is wearing. Red Mage was a mix between fighter, white mage, and black mage originally. They could use most of the same weapons as a fighter and wearing things like chain mail and scale mail were pretty common. They also couldn't cast the highest levels of black or white magic. They retained most of that in FFXI but tended to focus more on casting in the end game due to game design.

I'm not a fan of pigeon holing this class into being a caster and wearing caster gear. It shouldn't be just a caster. This class really does need it's own set of gear to be what it should be. Barring that they could either find a way to increase the armor value for red mages in cloth gear or find a way to give them int and mnd from the dragoon gear. Some sort of cleric stance like ability would probably work.

I do like the idea of adding in other stats to all the gear and making them somewhat relevant again. I am pretty sure that's how 1.0 gear worked.