You should do some actual research on studies in this area before you trot out unsupported pop psychology because literally everything you wrote is exactly opposite of what has been shown to be the case.

Multiple studies have shown that over time most survivors do not find closure through execution and those on death row suffer more psychological stress than those serving life imprisonment. Additionally executions have shown to have long lasting negative psychological impacts on those that witness or have connection to the event, even those that are victims/survivors.

Yes I know what you wrote sounds like it should be true but it is entirely contradicted by decades of studies all over the world and is not supported by evidence.