Well, this kind of approaches the question of what we use the death penalty for in the first place. If it's some sense of justice or so we can all stand up and cheer together when the bad guys get it in the end, then the problem of no one reporting the crime or no one committing the crime rather means we've failed. We don't get to execute anyone. How disappointing.
On the other hand, if what we want out of the death penalty in the first place is to deter the crime itself then it's rather a good thing when folks are afraid to commit that crime in public. Can we agree that in that case they'll be even less inclined to commit that crime in private as well? And if there's no incentive to report the crime to the authorities, as you point out, we really don't care. As long as folks are persuaded not the commit the crime, we don't even have to catch them at it on the rare occasion that they do for this whole process to have worked.
This is why I usually get kinda :squint: when people jump to hysterical conclusions about cameras in bedrooms whenever this kind of subject comes up. We don't have cameras in people's bedrooms (or any other rooms) to catch them at any other crime. Because we don't even really want to catch them all that much. That's not really the goal. The goal of criminal law is deterrence, right?