I can pretty easily see Redmage as a DoM DPS. Unlike BLM, RDM maximum DPS comes from mobility instead of remaining stationary.
Rough RDM concept
(just using 'En' prefix as a demo naming convention)
Enfire1,2,3 being melee range spells (sword) (they make a combo),
and EnLightning1,2,3 being instant cast caster spells (they make a combo, too. EnLightning spells deliver higher potency when outside melee range <like MCH/BRD DPS in PVP>).
But then throw in low-recast OGCD gap-maker & gap-closer abilities with better DPS and/or Debuff combos like Enfire1 > Enfire 2 > (gap-maker) EnLightning 3, or EnLightning 1 > EnLightning 2 > (gap-closer) EnFire 3.
The healing side of RDM kit could just be party Support CDs, like how we've got Mantra, Divine Veil, and others.
Isn't this all a little imaginary though? We're not even sure 4.0 will provide new jobs, are we?
IIRC the only Q@A LL I recall is (paraphrasing), "..we're not looking at new jobs until 4.0." Which is rather ambiguous, could mean new job possibly in 4.0 patch, or just some time in the 4.x patch cycle in it's entirety. But then again I've missed some of the more recent LLs. (And there was that "which first, Red or Blue?" dialogue bubble during the anniversary event)
edit:

Originally Posted by
KrenianKandos
I wouldn't mind them delving into FFT classes, honestly. It was one of my favorite Final Fantasy games so I'm all for it.
QFT, FFT being the best isn't an opinion - it's a factual statement