I have never thought of a DRK as a self-healing job, infact, I cannot think of any instance where this is the case (I have not played FF11, so it could come up there), DRKs are however known for using their HP as a resource, which we all know is a bad idea, so MP is used instead. Nothing about DRK suggests self sustain.
Evasion is a very bad way to mitigate damage ad it is all RNG. You either evade, or you do not and if you do not evade, you take the full hit anyway. All jobs can parry and only PLDs can block. GNB does have Camouflage which does increase the parry rate by 50% whilst also giving 10% damage mitigation (need something incase the RNG doesn't work). You could make a point that they could give GNB an ability that increases parry rate to 100%, similar to PLD and Sheltron, however, parry does not work against magic attacks, whereas blocking does. So, is it really a good idea? As for the DoT idea, I can't see it being too useful depending on a few things, the main one being, how long is this DoT going to last. The longer it lasts, the more it just become an annoyance as the damage is spread out too thin to be a threat, too short and they still take heavy damage, add to this, you are still getting hit by other things, the DoT damage could soon add up to be a bigger pain than intended. I cannot see it working as a general mitigation tool, however, it could be interesting as the invuln button.
This probably stems from 2.0 where Warrior was originally meant to be the sustain tank, using higher HP and a reduced ability to reduce incoming damage, the intent being they took the attack and healed it back up. Originally, it didn't work out that way so it got some changes early on, and from that point on, it became one of the best tanks and still remains one of the best tanks. I think at this point, it would be weird to change it away, so it has kept this identity.
The reason PLD is the only one that feels like a tank is probably due to the fact it is the only one that you immediately think of as a tank. Take any job throughout the series and think of any that would fit the tank role. The first one to probably come up is Knight/Paladin. They are protectors, they have had defensive capabilities baked into them via innate cover, higher HP and defences, etc. They just slot right in. However, can you think of any other high HP and defence jobs? You might come up with a few after some thought, but it is hard. You almost have to reshape a job to fit the tank role.
As for the homogenous comment, you have to take into account each tank has to have access to the same basic kit, start taking away some things from this kit and it could mean the job falls out of favour and not considered for raids. The tanks are then using their DPS rotation to get their flavour out, which, all the tanks do play differently.