OK gang, let's unpack this "breathe off the tank valve" thing...It would be faster and better to ascend to the surface, than to try unscrewing the first stage and breathing out of a tank. Honestly, if you have the presence of mind and ability to take off your BC and tank, unscrew your first stage, and breathe directly off a freeflowing tank valve (???) while maintaining an appropriate rate of ascent then you are way too accomplished a diver to be making a rookie mistake like diving solo with no bailout / redundant gas source.
There are two modes of "total first stage failure" - freeflow mode and no flow mode, with freeflow being far more likely. So let's examine that mode first.
(1) First stage failed open - freeflow
There are two basic ways to handle a freeflow.
First, just keep breathing the free flowing regulator until you reach the surface, and
second, shut the air off with the tank valve and then meter it as you need it using the tank valve. No big deal either way, and certainly no need to take the reg off the tank.
(2) First stage failed closed - no flow.
Now, here we are with a reg that ain't flowing, so we just take it off the tank, right?
WRONG!
If it ain't flowing and it ain't delivering, then the hp chamber's full of hp gas, shutting off the tank valve won't release it, and there's little chance you'll be able to get the first stage off there without a pipe wrench!
So whether you can successfully breathe off a tank valve (it takes practice!) or not becomes moot.
Rick