I've chosen to gear as much as possible towards mastery. As a protection warrior, mastery increases your chance to block (and critically block). I definitely agree with you on the way tank damage and tank deaths happen now but its not as simple as taking less damage over the fight.
If you gear for pure stamina, or at least largely for stamina while ignoring avoidance/mastery, you well get hit (for full amount) noticeably more often. The way a healer copes with this is using bigger heals more often just in case they get too far behind on tank healing. This is of course very mana inefficient.
If you gear for pure avoidance (dodge and parry) you will take the least possible amount of damage throughout the fight. This isn't necessarily the best solution though. High avoidance means that tank damage looks like - avoid, avoid, avoid, followed by a string of unavoided hits. The tank drops low suddenly when this happens and healers end up using expensive heals because the damage has came quickly and you want to pick the tank back up quickly in case another burst of damage comes in the same way.
Per point, you get higher % chance to block an attack (mastery) than you do for avoidance (dodge or parry). This means that if you stack mastery to high enough amount, you can smooth out the way you take damage. You will take more damage over the course of a fight than an avoidance stacking tank, but you will be easier (more predictable) to heal and thus the healers can comfortably use their cheap heals on you with the occasional bigger heal if they think its needed, and end up saving more mana this way. Block was reworked to be a guaranteed block of 30% of the damage, which is now why it "smooths out" incoming damage.
Gearing for mastery this way also means that you can obtain 75% combined block, dodge and parry chance and when you use Shield Block (increases block chance by 25% for 10s) you are guaranteed to never take a full hit. This in effect is a 30% shield wall to physical hits. In later raid tiers it may be possible to gear for 100% combined block and avoidance, and could even be absolutely necessary in the way that warriors would keep up Shield Block the whole time in TBC, to make sure a portion of any hit taken was blocked (avoid crushing blows).
Someone will have to confirm things like chance to be missed (if it still exists) but this is the theory behind gearing for block and avoidance. But remember that stamina is never a *bad* stat, some heroic mode bosses are bound to burst pretty high and you need the health to survive certain encounter mechanics. I would probably also not favour a particularly small amount of mastery over an exceptionally large amount of stamina, in the way that in ICC we chose any amount of stam or armour over huge amounts of avoidance.
Hope this helps.