WAR damage is lacking

[Reynhart]

PLDs having a "simple" stable rotation, WARs having "primal" stack generation and use that allow for big hits, and DRK buffing various abilities and attacks with Dark Arts are the primary things that distinguish the 3 tanks from each other.

First problem with that. Nothing you actually describes as any real impact on how you tank. All of these refers to how do they do damage.

Hallowed Ground/Holmgang/Living Dead is another example.

But, most of the time, they're still used in the same way and at the same time. And they don't really matter when you chose which tank you'll want in your party. The "tanking" gameplay could be much more unique between the three tanks.

Lets says SE wanted to give all 3 tanks a full party protection skill like the Paladin's Divine Veil.

Then you'll have people beginning to crunch numbers to determine which "party protection" skill is the best, depending on potency and CD...and then still choosing WAR
As a reminder, they already have a "party protection" skill. For WAR, it's called Storm's Path, and for DRK, it's called Delirium, since party wide AoE are frequently magical.

WAR being the dps tank, PLD being the physical tank and DRK being the magic tank are kinda where the whole imbalance problem comes from.

Not really. The imbalance comes from WAR's main contribution being offensive while the other two are defensive. Let's get real, no one cares what any tank bring on a pure defensive spot, since even the lowest defensive tank needs to be able to main tank anything. So, you have to design three ways of contributing offensively to the party.