For me, it's one that uses magic.
DRK's main mechanic is managing MP for Darkside and Dark Arts. The other aspects of its toolkit are really weak in defining it. You can't really say that it's defined by being a melee and then say that WAR is more unique, but more importantly a casting tank would require a method of casting without interruption. This game is simply too fast paced to accommodate a caster tank right now. It's why people raged about Clemency and got the change they did, and also a big reason why it's still not used that much.
Using a stance to convert caster gear to tank gear isn't as simple as Cleric. Cleric merely swaps MND with INT, so yes you could swap INT with STR, but where does the extra VIT come from? Do you want the mage tank to have a tiny pool of HP? If you boost their base HP, their HP will quickly be dwarfed by the increase in ilevel. What stat converts into their defense? Even if you do this, it would mean tanking w/o tank stance becomes even worse than what tanks do now since they now have caster defense/HP without it. Of course it can be done, but It's more complex than you're suggesting.
What is so wrong with a RDM healer? RDM are known to be jacks of all trades. That means they shouldn't be able to take hits like a warrior or paladin, but should have some means of shielding. They shouldn't have the dps of monk or dragoon, but have decent dps along with a rapier. They shouldn't have the healing of white mage, but should be able to heal a party. To me this clearly points to it being a frontline melee healer. Take all your ideas and place them on RDM and it starts to make sense to me. DNC should be a frontline support job in the future.
Blue Mage could be almost anything. I do agree that it could be a tank, but I think it would take a considerable amount of effort in comparison to something like Samurai. The gear/defense problem is not one to take lightly. Samurai can wear all current tank gear without any real questions. Perhaps the only gear that looks odd is the traditional knight looking sets and the Gerolt Masterworks set, but I doubt anyone would really be bothered by this. Blue Mage has less of identity, but I still don't see them wearing the majority of tank sets that are currently out there, whereas it could easily become this frontline caster DPS that everyone seems to want when they say they want RDM as a DPS.
Why is DNC as a frontline healer an okay option, but RDM is not?
Why is RDM as a frontline caster DPS an okay option, but not BLU is not?