First off you will be using CDs so you will barely take any more damage.
Secondly, you get so much vengeance that you basically keep yourself alive. You will not die because you take any extra damage and you will not require a single extra heal either. That is the entire basis of this argument that people have absolutely no idea how tank healing and tank damage in-take works. You will not need extra heals for standing in annihilates and the only risk of dying is bad CD planning.
Same goes with the DPS argument. Just because a group got enough gear to down a boss does not mean they are utilizing their classes. You dont say in threads of people asking for Garrosh HC help "You got above 565 average, L2P" or people asking for help about siegecrafter heroic "You got above 550 average just play your class good".
If he can do anything to help his raid, then he should. Saying that "DPSers should fix the dps problem" is a very single minded point of view. If he as a tank can also solve the dps problem then why not? A tank doing 100k extra dps or a dps doing 100k extra dps is the same for the raid. In current raid design DPS is just as much a healer and tank problem as it is dpsers.
There is also the possibility of him being far better than the players he play with, which is what it sounds like considering he plays in pugs with alts. In ToT I raided with a raid team that if I look at it without bias, I was miles and miles beyond everyone else in that raid team in terms of class throughput and raiding skills. I got more rank 1s in that tier than the entire raid got ranks at all, our world of log ranks were 95% mine. Now of course that does not matter, I enjoyed playing with them and I had a lot of fun. Instead of asking the others to step up, I looked to further improve myself. Being a tank I could often off-set the dps we lacked. Just because our dpsers did not perform as they should did not mean I could go the extra mile and push out more dps.
As it is in his scenario, it is not realistic to expect pugs to perform at a high level. If he is a great player then he can perform at 110% to off-set the other players therefor helping to get the kill.
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We had about 260 wipes on Garrosh Heroic and I never died once to annihilate even though I soaked it every time. I died once when experimenting when it was already a wipe though but I do not really count that as it was only 5 people alive at the time.
1/15 is a way to high chance to die in my opinion for that gain, but as you said, with better CDs you should be able to bring that down.