They had this in ARR and HW (it was called Cleric Stance) and it was removed because it was something that on paper may look good but in practice meant a lot of wipes if the healer was in "DPS phase" when healing was needed. It works for a DPS because DPS Jobs don't have a second essential task. Their task is "Do damage". Tanks and healers each have a second essential task they must achieve for the party to succeed, which are mitigate damage (in theory, hold threat, but that's automatic at this point) for tanks and heal the party for healers. When BLM goes into Ice for several casts, it's not going to immediately cause the boss to enrage and wipe the party. If a healer is caught in damage stance (higher damage but lower healing) and the boss goes into a high damage phase OR some of your party members screw up and need emergency healing, people die and wipes happen.
They also used to have this with tanks (threat increase and damage reduction tank stances vs damage increase stances) which weren't AS detrimental (a tank in damage stance using CDs could get their defense high enough to still survive big hits), but were removed for a similar reason.
Because both of these things were in the game and removed because they were seen as bad (and incidentally generated a lot of toxicity), it's unlikely they'll be re-added. Balancing an essential task (survivability/healing) against another (damage) tends to not be good design in practice, even if it seems it could be on paper. Again, BLM in Ice stance (for 3-5 GCDs) isn't causing the party to wipe. Healer in damage stance during the wrong time can cause party wipes. I think that's the distinction there.
EDIT:
Wait, what?
Meta has been AST/SCH since EW launch outside of a week or so here or there. And has been meta for all of ShB and SB before it.
I agree that the split didn't work out - so much so I think WHM needs a 60 sec CD ability (tack Proshell onto Confession stacks, easy fix there) and AST should get Noct back because...seriously, why not? It was more distinct as a barrier healer than SGE is to SCH anyway - but the meta is clearly in favor of AST.
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I don't entirely agree with your point as a whole, but how far can we carry this?
A Rogue in WoW works by building and spending Combo points, but in practice on boss fights, this translates to playing much like something like RPR where you build a resource and spend the resource. BLM (and WoW Arcane Mage) play with a similar ping-pong mechanic between burst and regen periods of their rotations. SMN (reminds me of Wrath and Cata era Ret Paladins in WoW) operates on a "It's off CD? Well then hit it!" mentality, which WAR operates SOMEWHAT similar to (if one isn't trying to hyper optimize, anyway). How is PLD's 1-2-3 1-2-4-5-5-5 1-2-3 1-2-4-5-5 1-2-3 6-6-6-6 7-7-7-7 just another variation of 1-2-3 and some oGCDs?
There's a point where you can zoom out to orbit, and then keep zooming out to where you can see the whole solar system, at which point every spot on the surface of the Earth will look the same as a kind of bluish haze...but that doesn't mean they're at all the same. Everything looks the same if you zoom out far enough, and every MMO combat system could be described as "variations of 1-2-3 with some CD abilities thrown in" if we go to that level of zoom, I think.
T-Owl says that WoW made the tanks distinct, but their mitigations are like FFXIV - different flavors of the same thing. "Choose between" Shield of the Righteous and the Holy heal on Protection Paladin isn't so different from a WAR choosing between Bloodwhetting or Nascent. The main difference is that FFXIV active mitigations tend to employ both together. And the distinction between WoW Prot Paly and tanky DK is kind of matched in FFXIV's between PLD and DRK - Blackest Night and Shelltron make a similar contrast. So does Heart of Corundum and Bloodwhetting. The idea that WoW's class design is so distinct but FFXIV's is samey doesn't really hold up when you look at them closely at all. Or even not at all - I play WAR and GNB and have PLD at 90; they all play distinct. RDM and SMN and BLM play nothing alike one another. MCH, NIN, and MNK (my other 90s) also don't play anything alike each other.