I think you eliminated half the equation. It's not that the jury doesn't agree on the death penalty, it's that the jury doesn't agree on a penalty, one of which is the death penalty.I agree, it is rather like two bites at the apple for the death penalty and given the seriousness of the punishment that just doesn't feel right. You know, one doesnt agree on death so we will find one that does. It just sticks in my craw and should anyone's no matter if they favor dp or not. The judge should make the decision after a hung jury
The goal when the death penalty is involved, is to find a jury that agrees on a penalty of life or death -- not one that agrees on death.
If you see each phase as distinct trial then it is completely consistent with how our system works. When a jury hangs, the person is retried (if the prosecutor chooses) until a unanimous verdict is reached. And so it is in this phase, the prosecutor can have a new penalty "trial" or can take death off the table and let the judge decide between life and LWOP.
I really like the idea that only a jury can decide to put a person to death. I don't think that decision should be in the hands of judge -- especially one who is elected.