Going to take what I said on another forum.
STR is a support for ATKP in the same way VIT is support for DEF.
ATK_STR/VIT|DEF
Let me put it like this. Let's visualize this without a bunch of numbers. VIT acts as a wall. STR is a latter. Your STR needs to extend against or over that VIT wall for Attack to get to the other side and combat mob's defense effectively.
So, in terms of Mobs that have these high amounts of VIT, it becomes more about STR to push that attack through into a higher DMG threshold. On other mobs where you hit STR softcap on, it's more ATK dependent to hit consistently higher. This is the reason why STR builds out parse ATK focused builds on Ifrit or any other high level / High VIT mobs.