Will depend largely on bosses ExtremePain. Having minimum EH's to survive encounters will still be our primary concern, but even in Sunwell where the same avoidance debuff was first implemented, avoidance was VERY useful for fights like Brutallus. As has always been said in the past and will always be said in the forseeable future: Gear/Chant/Gem for the encounter.
It isn't that much of the damage isn't avoidable, it's that the lethal parts aren't. Northrend Beasts for example. Impale and it's bleed. Both of which are considered physical, neither of which can be avoided. Icehowl constantly stuns the tank, eliminating all avoidance for that period of time. There goes a large portion of your argument.
Jaraxxus doesn't hit hard enough to warrant more avoidance. It's idiots standing in fire that kills.
For Anub'arak the lethal part is Freezing Slash (which also eliminates all avoidance) and melee swings while frozen, particularly during Leeching Swarm. The caveat to this fight is that the more health you have the more healing you do to him, so using that avoidance trinket instead of a stamina trinket is technically more ideal so long as you reach the minimum threshold.
Twin Val'kyr is probably the one fight in ToC that more avoidance is generally fine since 75% or more of their damage is from *melee*. That's the key word you need to differentiate with. Lumping everything in the "physical" school as avoidable isn't always right, particularly with a fight like Northrend Beasts or Anub'arak where there are bleeds or you get stunned/frozen.
And yes, the strongest advocate of stacking Stamina is the heroic mode right now, especially 25-man, as the spike damage you take that can't be avoided can be pretty huge.
The pain mistresses on jaraxxus hit pretty hard AND fast, so they're a great candidate for high avoidance too. You could probably tank jaraxxus himself naked.