The gear is ranked so high due to it's high stamina value, something us bears get the most bang for the buck out of.
Here is my real world testing thoughts... at least at the current level of raiding... considering I am in mostly Naxx heroic gear.
1. No polar for trash pulls. You want to use your gear that falls closest to the polar items in rank but gem/equip/enchant for damage, hit, expertise to hold the threat you need when you are AoEing this stuff down.
2. Patchwerk... by now you know to wear you polar gear and highest stam pieces if you are soaking the hurtfuls.
3. Don't gem/enchant your polar gear trying to get avoidance out of it. gem/enchant more stam, that is what you want out of these items when you do wear them.
4. Any fight you MT, wear these items. You won't have problem with single target threat and the huge HP pool helps with the various silence mechanics and what not in many of these boss fights.
5. The polar chest/belt/boots is a must have IMHO for any starting bear hitting level 80. It is too cheap to get these crafted not to have them starting heroics and 10 man Naxx.
6. OTing on bosses where you are controlling add waves you should be fine ditching the polar. I would also not use it on Gothik or Noth fights where controlling adds is very important.
I would use Polar on these fights...
Anub'Rekhan - If OT no need for Polar. (Insect swarm hurts, healer positioning, green goo)
Grand Widow Faerlina - If OT no need for Polar. (red too long or people want achievement)
Maexxna - (Everyone gets frozen/webbed)
Heigan the Unclean - (in case you mess up the dance... over and over)
Loatheb - (healer silence)
The Four Horsemen - (Meteor, bad party or OT placement even if for a moment, stacking debuff)
Patchwerk - Huge Hurtfuls
Grobbulus - If OT no need for Polar. - (Positioning, players that don't get away when injected)
Gluth - (stacking debuff, decimate)
Thaddius - (Players changing sides late)
Sapphiron - FR is reason alone
Kel'Thuzad - (void zones, icebolts, bad melee positioning)
So there you go with a short notation of the problem mechanics. You prob could tank more than one without polar gear depending on the experience and talent of your raid members but I see no good reason not to wear it as a safety precaution on those same fights.
I don't have any experience tanking Malygos yet or the 3 drakes up fight (although it is known you need uber HP for that) and the Vault fight is easy.