Holding the threat of death over people isn't the way to a "high-trust society." Maybe you think it's the way to something similar, but you have to give up the word "trust" because it doesn't apply here. If the only reason I think a man isn't going to rob me is because I will shoot him if he does, I don't trust that man.
A society which only has low crime because everyone is able to use lethal force to defend themselves and their property isn't one I would call higher "trust" than one that maintains the same crime levels without that threat.
I think that is the wrong way to think about it.
The end state is you can trust others because nobody even wants to or considers it.
Punishing violators is being proposed as how to build the norm that no one wants to steal.