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I think the Nuremberg trials show a decent example where the death penalty is justifiable.
For each of your points:
1) The victims of Nazi rule said they did it, they confessed to doing them(since they believe they were not in the wrong) and no one seems to oppose that view. Of course holocaust deniers exist but every claim they make can be easily disproven with empirical evidence.
2) Justice is not necessarily about maximising suffering. Most of the time it is about an acknowledgment of the crime and the imposition of a consequence that fits it. Death seems fair for genocide, no one gains from additional suffering.
3) Denazification was important and removing their influence was crucial to crumble their hold over the German population
4) No one wants to fund a Nazi, death is merciful and cheap
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