I'd just like to point out that having 1500 extra HP is like having a consistent 1500 HP damage absorption shield. Because overhealing is done regardless of how much HP you have. Actually, isn't it so that the less HP you have, the more overhealing there tends to be? Having more HP means more of that overhealing is turned into useful HP to absorb the next hit.
It's interesting to see how tank gearing in FFXIV is so radically different from some other games where tanks work their hardest to get even that 1% more mitigation to minimize the possibility of the worst case scenario. Tanks used to gear for the worst case scenario, things like back-to-back crits, tank buster followed immediately by an auto-attack crit, healers getting tied up and unable to heal for another 2 seconds, etc.
But in FFXIV, tanks seem to gear for the best-case scenario, i.e. healers always performing their best and always able to heal you up to full (i.e. the claim that there's always overhealing), you always time your cooldowns properly, you don't "need" the buffer health if your "good enough".
If you gear for best-case scenario, you gear for STR. If you gear for worst-case scenario, you gear for VIT. If you want middle ground and have the money, you overmeld and get quantitatively more overall benefit. It doesn't really sound that bad.
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Lastly, I'd just like to present this thought for the "faster kill argument".
Unless you're hitting enrage timers, a few seconds faster kill isn't "needed", it's useless, in the same way that you don't "need" that extra 1500 HP unless you're dying. The only time STR is "useful" is when you are hitting enrage timers or when that little bit of tank dps gain pushes a phase such that you avoid some critical boss ability---and in those situations, then yes you want to gear for STR to contribute whatever little bit of dps you can, simply because you would wipe otherwise.
In any other situation, that extra dps simply doesn't matter. It's as much e-peen as is higher HP.