Thing is that before shooting Salit, it might have been useful to discover:
a) Why he is doing it - what does he hope to gain?

If the information he handed over is so much more useful than either gunpowder or ship plans, how did he get hold of it in the first place? The gunpowder plans are zealously guarded, so anything equally dangerous to the Qunari's plans should also be zealously guarded - only available to a very select and trusted few. So who exactly was Salit?
This is also information that I would have liked to have got out of Tallis after disposing of Duke Prosper. I have mentioned elsewhere that I actually doubt a complete list of all spies throughout Thedas would exist, may be it was a list of just the ones in Orlais, which might still implicate a large number of people. However, given how valuable and dangerous it was to the Qunari cause, surely the most sensible thing for Tallis to do during the fight was just burn it. She is keeping hold of it because she apparently wants to go back and say to the leaders, "look how clever I am, I got this back", which if I understand their philosophy correctly they will respond to with "you were more concerned with yourself than the good of the people - you should have destroyed it at once". All they needed to know is that somehow someone got hold of information that they shouldn't have.
As for Hawke, they still have useful information that Tallis should never have divulged, why those names were significant. That is still something you can work with that you didn't have before - previously I only guessed that the situation in the Kirkwall Alienage might not be unique - now I know it. Whether I am a mage sympathiser or not, I do not want the Qun to take over, so from now on I will be on the look out for anything suspicious and if given the opportunity, introduce some counter measures of my own. I may not take the trouble to inform Celene (she may hear from Cassandra anyway), but I would certainly warn Alistair/Anora and suggest they improve relations still further with their alienage elves, plus perhaps introduce their own sleeper cells in the larger settlements to watch for any signs of suspicious activity.
Duke Prosper's actions were just the standard evil villain with no brains - the chevalier are probably very inbred.