1) Pld is more sturdy for a number of reasons. Shield alone is 5 to 10% reduced physical damage, native, without doing anything. While not of much use regarding tank busters, it does mean that pld are easier to heal outside of tank busters. In particular, when healers are focused on the party, the MT taking reduced "day to day" damage means healers are not as stressed by having to heal on two fronts at once. Another point is that they naturally get their damage reduction debuff while main tanking. They ARE going to use rage of halone. I am currently in a Pld/War group with no ninja. Having the Pld MT means we have close to 100% uptime on both path and halone debuff. That combination is the only one where you will have close to 100% uptime on 2 10% damage reduction debuffs. Reprisal from Drk is nowhere near 100% uptime, and should the War MT, then it is not realistic to maintain both path and halone up, since that means the MT not using his aggro combo while the pld use his.
2) The utility of pld cannot be understated either. You are brushing it off like it is nothing. As far as i know, almost any group went into A2S with a pld, and for good reason -- their sturdiness along with their utility are invaluable in there. Their aoe shield is extremely usefull to mitigate big aoe hits. Cover has lots of great uses; in A2S, covering a healer targeted by snipers really make some waves much easier. It is by no mean "mandatory" but it make some things soother. HG remain an amazing tool to push your group through your current struggling point to experience more of a fight. It is better than the Drk and War equivalent by miles, allowing healers to catch up when behind, providing a substantial DPS boost to the group by allowing an insane amount of dps from healers for 10 to 12 seconds, when it is not simply allowing you to bypass some hard parts purely and simply.
3) The dps difference is ridiculously low with other tanks.
Well what it seems is that you are trying to compare the dps of warrior that are tank dancing as much as possible with Pld staying in shield oath all the time. It really is a case of "GIT GUD" -- i'm sorry that's all there is to it.
Here is a video of a clear of A3S using a warrior and pld. The Pld did 650 dps, the warrior 778. That it despite the Pld main tanking the whole phase 1, the whole phase 2, and one more cascade phase in phase 4 than the warrior. Despite all this time main tanking (and thus having to use shield oath for a lot of it, and having to use rage of halone both for debuffs and aggro), there is only a 128 difference in dps. It is almost certain that should they have decided to reverse the roles: 1) the warrior would most likely not have done much more than the Pld, and 2) that would have come at the cost of a serious decrease in the safety of the MT.
You can continue having your head in the sand if you want. But the facts are here for you to consider. Pld is doing a MARGINAL amount of dps lower than the other tanks. It has only been significant for world first group on a3s without weapons, a feat that Yoshida admitted himself he did not think was possible. They won literally 1 second before wiping, if even that, they had to squeeze just EVERY bit of dps in, hence the choice of a Drk instead of a Pld. For anyone else, the difference is so minim it doesn't matter -- if anything it is BETTER to attempt A3S with a pld than a drk for anyone else, because it is a physical heavy fight, and Pld provide much more safety for the group compared to a Drk.
War just work amazingly as an OT. Their kit is super synergetic, as others have said, and being in an OT position allow them to maximize it, by keeping eye up 100%, having path usable as much as they want, making awesome use of unchained. War MT / Pld OT used to be higher dps, but that's not true anymore, now that War has their DPS stance and Pld have options to do more damage as a MT.
TL;DR: all three tanks are quite balanced at the moment. Pld offers the best Physical mitigation by far, and requires less day-to-day healing, while offering significant utility advantages over the other tanks. Drk offers the most mitigation in magic heavy fights, and provide slightly more DPS than a Pld as MT. War just work much better as an OT than a MT, not that they are "bad" at MT per say, but their kit can become ackward as MT (most notably due to the pressure between eye, path, and butcher), whereas it is pure gold as OT.
So you just have War best as OT, Pld best MT on physical encounters, Drk best MT on magical encounters. All three have their place in the wheel of life, and all is good.