Stamina is and always has been a great stat for a few reasons:
1) It gives a "cushion" as you mentioned to healers. The tank should have dedicated heals the entire fight, but there are a lot of encounters where the raid takes a lot of damage. Having a higher pool gives time for healers to catch up. Most of our cooldowns are 2-3minute cooldowns and we can use them like candy.
2) Secondly... magic dmg is not mitigated by anything except resists or cooldowns. Stamina being the best stat for magic (aside for resists, but as far as useful physical stats are concerned).
3) Thirdly, in the event that you are stunned, you will not avoid whatsoever. Stamina being superior in those cases.
I am not in any way saying you should purely stack stamina. I do find it to be incredibly useful, and as much as I'd like to stack avoidance as I used to in Burning Crusade... it's more viable to balance between avoidance and stamina. In my case as warrior, i reforge peices without mastery so that they do, and i gem mostly stamina, and mastery in those oddball sockets where the socket bonus is worth it.
Ruek - Prot Warrior <Fat Panda>
“Excellence is not a singular act, but a habit. You are what you repeatedly do.” -Shaq