I agree with your points (1) and (2); I disagree about your point (3).
If you reworded your point (3) to say, instead,
3) If you have predetermined that the PCs may not die then you need to have a mechanic or role-playing device to overcome bad luck and/or the effects of poor choices.
I could agree to that. I don't think that it need be a story-telling game.
Why you don't want the PCs to die is of no importance to the conclusion;
that you don't want the PCs to die is of paramount importance.
Of course, I would argue that it is better to never allow a potential consequence for failure that you are unwilling to play through in the event of failure in the first place. IOW, if you are unwilling to allow the PCs to die, don't set up a situation in which they can die.
I'm not big on the so-called "illusion of choice". I am less big on the "illusion of consequences". If you don't want the PCs to die, I would prefer the GM be up-front about that, and that there is a table consensus on what to do when the dice call for death.
The only difference is that they recharge every day instead of every encounter.
That is a separate thought, and one I very much disagree with.
EDIT: BTW, your post above (and others) show evidence of the fallacy of the excluded middle. You seem to feel that either (A) you need a mechanic to save PCs or (B) you are running a killer dungeon. I hope that is merely hyperbole, and that you realize that there is a very wide range of options between the two!
RC