FFXIV's Warrior wouldn't last a single trash pull in a WoW dungeon. The type of self healing it does only works in FFXIV thanks to the content design. As I've stated before, the way to go about it is to overcome the job design with content design, something Square Enix achieves very well with savage and ultimate, but not so well in dungeons.

Most players sub for the new story stuff, and then unsub until the next major patch. These players don't frequent the forums and they outnumber raiders 10 to 1. The minimum ilvl for dungeons is like way less than the previous expansion's best in slot, because these players only take whatever dungeon gear they get and don't even know better gear exists. If Square Enix overcame the job design in dungeons, these players would be unable to contribute to the party, much less figure out why they can't make progress, which would frustrate them and make them just give up. The way to break away from this state that dungeons are in is to stop tying the dungeons to the story. That would free up the devs to make the dungeons more challenging, and also more rewarding.

When you see a warrior go full immortal in dungeons, it's because they are using their cooldowns correctly AND extremely overgeared. If you were to play the job at minimum ilvl in the dungeon, which I've seen plenty of warriors who do, it's a much different story, and even a well seasoned veteran playing warrior in that state has to pretty much blow everything just to pull wall to wall. The dungeon balance is centered around doing the dungeon at the minimum ilvl. Which is something many players take for granted, as was made obvious via Dawntrail's dungeon design (those birds in the 97 dungeon hit like a truck, even when overgeared).