there is a fundamental disagreement here.
'Doc thinks that there is no actual "unavoidable" OOA. But Pete doesn't believe in double failures - because those can, and will, result in a real, honest-to-god OOA that is not anyone's "fault."
(Double failure defined - your first stage fails, and THEN your buddy's does. Or you have TWO first stage failures with redundant kit. Or you have a first state failure AND a buddy who isn't. Etc etc etc.)
I, on the other hand, while accepting that MOST OOAs are due to inattentiveness, accept that double failures DO happen. They are rare, but they occur.
I am unwilling to accept a sentence of certain death when one occurs. I prefer to consider expiring only when no other options remain, irrespective of how "ugly" those options might be.
Roakey - false; it will be EXTREMELY difficult to breathe with a burst LP hose, but it IS possible. For the "maximum effort" take your reg off your tank and inhale through the second stage. You WILL get airflow, but not much.
The bigger problem is that a burst LP hose will drain your air supply EXTREMELY quickly. It is far, far worse than a HP hose failure, which actually drains your tank quite slowly. If you lose an LP hose, you may as well consider your tank gone, irrespective of whether you can get a breath or two, because for all intents and purposes it is.
If you can reach the failure and kink above it you can get the IP up high enough, and slow the air loss enough, to get usable air. But if not (e.g. its at the reg swege) then you're screwed. The bigger problem is that you have - literally - seconds before your tank is empty when this happens.
If you want an object lesson on this take off your second stage from its LP hose, put your reg on a low tank (say, one with 500 psi), secure the hose end so it doesn't thrash around and hit you, and open the valve. Measure the time before the SPG reads "zero". Hint: you'll need a pretty high resolution stopwatch and a quick finger
You can try to breathe off the remaining second stage if you want too - you'll find its barely possible. And oh, by the way, your power inflator won't work worth a hill of beans either.