Dukat had to die. Damar was marked for death because he killed an innocent (Ziyal). No amount of personal redemption could make amends. And Weyoun always gets killed. Don't worry, of course they have his template squirrelled away in the GQ.
Ziyal committed treason against the Dominion and Cardassia. She assaulted a guard, was an accessory to the death of two Jem'Hadar and freed 5 or 6 criminals from custody as well as committed wilful damage to a Cardassian/Dominion run facility. Damar was probably well within his rights to execute her under Cardassian or Dominion law.
I think it would have been interesting to have Damar survive but if he does that brings up a whole range of issues that they wouldn't be able to deal with given the war ended in the last episode. Easier to just kill him off and close the door.
If he lived you have the question of whether any of the allies try him for his service in the war. The Cardassians might even want a go given Damar was part of the coup that led to the war or his work as a terrorist/freedom fighter and the deaths he caused then. Plus then you have someone who might contradict the events that led to the Romulans entering the war, what would the Feds do to keep him quiet? You could probably get a novel or two just out of Damar post-DS9 if he survived.