Mark - the point is if there is no air left in the tank there is nothing to use. In cold water as Mike said it could be a first stage freeze that will clear quickly if shut down. It could also be an o-ring blow out - internal or main tank ring. Shutting down the tank means conserving what's left in it before the first stage comes into play. In a free flow situation you can get air through the flow, turn it off, ascend a bit blowing your bubbles to keep your air passage open, turn it on and repeat. Even if the first stage is completely unusable because of a tank O-ring for instance you can breath directly off the tank by feathering it in the same way.markfm:Kim -- What "massive 1st stage failure" is going to be solved by turning the valve off?
If the air in the tank is not going to be useable, I'd rather not be spending the time, energy, remaining breath in my lungs turning the valve off. There's either an alternate air supply to provide time to do mechanical mucking about (buddy, pony, isolated second tank), else it's time to do a Hail Mary ascent. Are you thinking about something like a first stage freeflow? What's the actual likelihood of that clearing by one or two on-offs? (risk/benefit -- since it takes multiple turns on the valve to shut it off, we're talking a serious number of seconds here. I'd personally hate to spend 10 seconds of my last breath trying to turn the valve off then on again, only to find I'm still hosed, that it was an o-ring blowout or some such, not cured by an on/off)
(I'm asking this out of real curiosity, a serious question, trying to understand a major failure that's going to deplete your tank in seconds, yet can somehow be cured by turning the valve off, and the remaining air in the tank will somehow then become accessible again.).
Now I'm not saying that this is ideal...it's not. The point is that if you can turn your tank off (and then on again) quickly enough to save the remaining air in it, it gives you more options to try. If the tank is empty and there's not another one close....you'd better hope that what's in your lungs will get you to the surface.
IMO being able to reach your tank valve is important using a single tank - or doubles. Even the other one Mike mentioned - jumping in with your tank turned off - can be a death sentence if you can't turn your tank on yourself. I believe this latter one has actually happened to quite a few people. Think about it....drowning with a completely full tank of air strapped to your back!
edit: Mike already seems to have addressed it.