Redmages ARE fighter-mages..yet early on SquareEnix has kept the, restrained by using mp pool, lowered skill levels, and constant casting cycles. They eventually gave RDM's a break with composure. However, this job has been extremely closely watched and nerf repeatedly.

Most RDM play styles are the same... Conserving MP means we are not using our tier III and IV's despite these being stronger than the few wacks of our swords and or occasional weapon strikes. We let ourselves become haste/refresh bots in normal play areas(NON-Abyssea).
Our nukes are just as strong as a bluemages, if only because we don't suffer from the same dangers of TP gain and enimity gain. Sure, a blue Mage can spam 2-4 physical spells and do over 2-4k damage but good luck getting a mob off him.

I would like to see more RDM self spells though. Not necessarily haste II(issues after all). But, things like "Magic Arrows", Phalanx III(target cast), Enspell III(think Rune/MP consumption per swing), "Magic Phalanx", etc.