Normal failure rate for the BMW [rear] diffs is close to zero under, let's say 150 k miles.I didnt hear of any E53 diff failures,let alone in this spectacular fashion,self-destruction.That is why hearing of a few E70 diff failures within a week is a pattern.I dont know details,but the diff usually goes noisy,clunky,etc but still the car could move under it's own power.
Regarding hard launches:
-the transfer case will suffer much more than the diffs in such a situation.It is far more fragile than the diffs and will brake much more earlier. 400 lb/ft of torque split between the axles is not enough to break WELL engineered parts.
-I have done many hard launches with stock diffs on my drag days.If you have a wheel hop you brake a tooth.The diff is noisy,sometimes clicking badly,but the car still moves on it's own.