I figured this thread was starting to devolve into the OP's personal whining rather than actual proper theory, and this explains why.
You're a new scholar. In average gear. You are worried about fight length and worried about running out of mana.
No Scholar should ever run out of mana unless they're managing cooldowns incorrectly, DPSing hard, having to resurrect people or terribly geared.
Even in i154 a scholar should be able to find a few cooldowns to DoT up a pack and bane them. Scholar AOE dps is much much bigger than the difference between a tank going vit vs str accessories.
All of the sweeping statements you've made are from a few runs where some bad/lazy tanks have had issues and you've equated it with Vit/Str. Strawman arguments all over the place. Good tanks are good, bad tanks are bad, the best tanks choose their gear setup as appropriate to the lineup of the party. A paladin in a group with a BLM/SMN/SCH would probably be better off going heavier vit and pulling gigantic packs because they'll be mostly Flashing anyway and doing much lower AOE dps compared to the rest. A Warrior would most likely always be full strength.
There's 100% truth that a bit of extra vit on the tank should allow a few extra seconds of DPS on a healer, and for a scholar who wants to throw up 4-5 cast times for maximum AOE dps on a pack, it really sucks to have a tank with 14000 hp who needs a heal after 3-4 gcds. Yes, it depends on gear level, and once a tank is in 190+ gaer on the left side then yes, go strength. I'd never want to see a fresh 145 tank going full strength and pulling huge packs though unless the group was prepared.
If you're worried about -running out of mana- in a 4man instance, then it's nothing whatsoever to do with whether the tank runs vit or str, and it's purely coincidence. They're managing cooldowns incorrectly, or you're healing incorrectly. The 15-20% extra tank DPS gained from going glass cannon compared to full vit should never be the difference between killing a pack fine and the healer running out of mana.