When a boss mob attacks a crit-immune bear tank, four things can happen: Miss, Dodge, Hit, or Crushing Blow. Misses and dodges are great, of course, and with enough defense and agility it's easy to push our avoidance to over 50%. But 15% of every attack from many bosses will be a Crushing Blow, and that Crushing Blow will do 1.5x normal damage. And there's nothing a bear can do to avoid it.
The only defense bears have against crushes is to get a bunch of armor and hit points to soak the extra damage. I'm close to 75% armor against bosses now and raid buffed I'm well over 20k health. Even so, I have trouble on a heavy melee hitter like Tidewalker. The average damage / attack I take is about the same as our best geared prot warrior (4000 vs. 3900). But 30% of the hits I take are crushes, averaging 5250. And it's not uncommon to get crushed two or three times in a row. The resulting spikey damage profile demands a lot of proactive healing. By contrast, an uncrushable warrior or paladin takes more predictable damage and can be healed more reactively.
There's also a terrible irony in bear gear: the better it gets, the higher the proportion of crushing blows we take. The way the Attack Table works every 1% Dodge we add means we have 1% less chance to take a normal hit. But we still have a 15% chance to be crushed, and there's really no practical way to reduce that. So my 50% avoidance means 15/50 = 30% of the incoming attacks will be crushing. If I got to 60% avoidance then 15/40 = 37.5% of the incoming attacks will be crushes. Put it another way; avoidance doesn't help bears with our biggest problem on bosses, crushes.
So should bear tanks give up? Of course not. We can still tank big crushing monsters, but the healers need to be a bit more aggressive about queuing big heals early. And while warriors and paladins can be uncrushable it's not particularly easy for them; there may be cases where you'd rather have a bear with lots of threat and armor. And tanking the big raid boss is only part of the game; tanking trash matters too. Trash mobs can't crush and the extra armor and threat generation of bears is a big help. But for a big crushing melee mob, your prot warrior friend is probably a better choice for the main tank than you.
The best news of all is that not all bosses crush. Apparently many of the BT and Hyjal bosses don't crush. And there are rumours that Blizzard is looking at reworking the crushing blow mechanic because the current system is too random. On the other hand, if it weren't for crushing blows then druid tanks would be completely overpowered. So who knows how it will balance out in the end.
PS: Does anyone have a complete list of which bosses crush?