This is a rather unusual take. "rage, vengeance, destruction" are what I would associate with Warrior, not Dark Knight. Also, "parrying with their weapon" I'd associate with PLD and GNB, and to a lesser extent DRK. You can't really parry all that well with a massive two handed axe...
DRK should be a shield focused tank more than a healing one. In normal FF lore, and in the general "unholy knight" archetype, they don't tend to heal themselves. They tend to use their health to fuel dark magic attacks. The sort of subtype dealing with blood magic might use drains, but that's not exactly what DRK is for the MOST part. Its lore is using darkness to shield people (basically like REDACTED did for the planet, if you think about it)
GNB is the closest thing FFXIV does have (and likely will have) to a dodge/evasion tank. Dodging doesn't work well as a mechanic because when it "misses", you get splattered. RNG hell. But of the tanks, GNB has the most parry related skills, which makes sense given their lighter armor and focus on swordplay. PLDs also have a high defensive option with block from their shields and parry from training with swords. The GNB identity is being a high speed/focused tank, with a bit of evasion, and a lot of swordplay. Also a gun.
I think WAR's thing with its self-healing should be more thought of as "advanced Second Wind" and "Adrenaline Rush/Fight or Flight" (despite PLD having an ability by that name, WAR is the one that leans into the aesthetic). You're thinking Man-At-Arms type Warriors. The FFXIV WAR is clearly much closer to a Berserker. And Berserker classes tend to have a TON of self-healing and health boosting type attacks.
Healing for PLD makes sense, but not for DRK. Dark magic is about inflicting damage and status effects, and rarely, mitigating damage (shielding) not healing.
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I will say that they are all different and there's some homogenization, but PLD is the holy warrior who shields, defends, supports (buffs), and (with some limits) restores/heals. WAR's motif is that of a berserker with some capacity for boosting morale with their superhuman feats (hence "healing"). GNB is an aggressive tank with a high speed of attack and augments defense of self and party members with its special weapon (stuff like Auroa is supposed to be a special type of shot from the gunblade, I believe). And DRK is an armor clad warrior that turns darkness to defense and enforce justice on the forces of evil, cladding themselves and their allies in shields of darkness to protect the weak while wielding the darkness to inflict damage upon the unjust.
Each, presently, fulfills these roles pretty much to a T, honestly.
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EDIT: For the record - what I mean by DRK being a shield tank is barriers/mitigation (like how SCH/SGE are "shield/barrier healers"), not like PLD carrying a shield to block with. So "barrier tank", if you prefer. PLD also gets some of that from Holy magic being more defensive in nature. DRK should, all things being equal, be a bit more offensive and debuff focused while PLD is more defensive and buff focused.