I would say that staggered damage also can synergize with delayed healing, since it gives you more time to allow that delay time to pass.
Also, I think it's interesting to assume how the stagger mechanic could work mechanically. I think the way that might be most FFXIV friendly would be that AST provides a buff that lasts for 10 seconds and reduces damage taken by 20%, storing that reduced value; then when the duration ends, that accumulated damage is taken over the next 12 seconds, and that would give you more time before you have to deal with the damage as well. That would prevent the effect from triggering a bunch of DOTs that bloat the buff/debuff limit on the party if they get hit a bunch of times during the effect duration. Could you imagine a tumult situation?