Yes, I really just did commit that title atrocity. It amused me, which is the only way I judge success.
Stamina stacking has been pretty common for tanks for a while. Stamina was generally seen as the default go-to stat for any tanking class at least throughout the Wrath of the Lich King expansion. It was the best way to increase effective health, which was ultimate in tank survivability.
I think, though, that Cataclysm has changed that. The only benefit to increased stamina, really, was the initial buffer before dying. Health pool measures only one thing: How much damage you can take, without healing, before you die. That's it. That was useful when most tanks had between 20k-60k (depending on when in the previous expansion we're talking about) and hits could take 10-20k health. An initial buffer to allow tanks to take some hits before healers stabilized things was valuable.
However, Cataclysm has completely changed the landscape in terms of the "spikiness" of encounters. It's a combination of overall size of default health pools (the health you get from level and unmodified gear) and bosses having less damage potential per hit, generally, if mechanics are obeyed. Tanks are no longer at any risk of dying within two to three bad hits. That means the value of an initial buffer has been reduced massively.
Let's take an example. An average raid-ready tank will have around 10-12 gem slots available. Let us say this tank gems straight stamina (and is not a jewelcrafter, so has no access to Chimera's Eye cuts). At 12 gem slots, with a +60 stamina gem in each, this adds up to 720 extra stamina. Each point of stamina is 14 extra health, so the tank gains 10,080 extra health. The average raid tank has around 140k default health, so the extra from gemming pushed him or her to 150k or so.
What does this mean when fighting a raid boss? It means only this: the tank can absorb an extra 10k health before dying if he or she gets no heals. That's all. As soon as the tank falls below 140k health in this example (i.e. essentially the first time the tank takes damage), the value of the extra stamina is gone. After that, the entirety of his or her ability to survive until the end comes from the tank's own avoidance and mitigation and the output of the raid's healers. Total health pool has no more impact.
In Shocking News, Health Is Not The Same As Mana
Stamina for tanks is not akin to intellect for casters, because total health pool does not have the same effects as total mana pool. Even leaving aside the fact that intellect has other benefits (spellpower, most notably), there are key mana regeneration mechanics that operate as a percentage of total mana pool. Therefore, having a larger total mana pool has a direct relation to longevity of that mana pool...it's not merely an initial buffer.
Total mana pool would be nothing but an initial buffer if the only mana return that existed was MP5, as that would be a rough analogue to healing. Healing works as raw numbers, just as MP5 does, not as percentage of total health pool. Therefore, the total size of the health pool (in the universe of normal tank pools...no tank is going to be sitting at 30k total health nor is any tank going to be sitting at 1 million total health) has virtually no impact on the longevity of the health pool. Only things like dodge, parry, mitigation (armor, block, etc), tank skill in employing cooldowns, healer skill and healer mana really have significant impact on the longevity of a health pool.
Healer skill and healer mana are not within the tank's control and tank skill is not affected by gemming and enchanting choices. Only avoidances and mitigation are, which is why those should be the only focuses of gems and enchants (this can include mastery, of course, since tanking mastery largely seems to be mitigation-focused).
So Is Stamina Useless For Tanks?
Short answer: Yes.
Long answer: ...Yes.
(Okay, to be a little less glib, by "stamina" I mean the stamina acquired from gems and enchants. The stamina you get from your gear is necessary but that's something you get automatically. Thanks for reading. I'm going to end the piece on this parenthetical comment because I'm a writing rebel.)