How would you design Red Mage in FFXIV?

[Gormogon]

You're right up to a point. It is impossible to have a balanced melee/nuke/heals hybrid in an MMORPG. There's simply too much to take into account if you are truly trying to make it an even split between the three aspects. And you're right, such a hybrid will never see endgame, and if they do it'll be after getting pigeonholed into a role that chances are the people who rolled said hybrid did not want to do. For FFXI's RDM it was buffbotting; for WoW's paladins it was healing.

That said, it is possible to have a DPS with utility in the form of limited healing and some buffs that are easy to cast and easy to maintain. The combat model would still favor DPS over heals while making heals possible but extremely limited. Going to WoW's paladins, if you specced Retribution you spent your resources smashing faces, but if you felt the need to heal you could...at the cost of most if not your entire mana bar casting two or three heal spells that healed nowhere near what those spells would do coming from a real healer. It was fairly balanced, was still found wanting in competitive-level PvP (contrary to some predictions, hybrids did not rule the PvP universe when they were made combat-viable), nor was it topping DPS meters in raids. It was good enough for justify their DPS spots while still being considered hybrids.

That's the appoach I would like to see the devs take.

Take into consideration that SMN's can heal and BLM can cross class a heal as well. They aren't great enough heals for them to be considered healers obviously but it's enough to stall and if it's a blm/smn + paladin healing they can easily sustain the fight long enough as long as they manage their mana in dungeons, keyword dungeon. Not saying it should be done but it's a potential alternative to some content in that low percent and the healer is struggling.

As for a Red Mage even with double cast it shouldn't be much of a game changer in PvE since double cast will most likely be on a 30 second plus cooldown and in PvP will only be as annoying as dealing with a scholars fairy.

People that complicate a system, mechanic, design only have themselves to blame for believing that something isn't possible. Every FF archetype is possible in FFXIV so far the only restriction when it comes to creating classes and jobs is self-imposed restrictions not something as legit as a "time investment" to creating a class, gear, etc. The biggest offender is the whole job has to fit in with the FFXIV "lore".