I think each ruling combination has benefits to specific Inquisitors, and adds to reply value.
My male human mage respected the sovereignty of all nations, and believed that interference in Orlais' throne was uncalled for. So he made the three-way deadlock possible.
My female elven mage didn't care about the humans or even the flat ears really, but she felt that Briala might lead those elves to a better life, which could in turn lead to more of them turning to the Dalish pantheon. She also hated Celene for her past actions and general incompetence. But she also wasn't about to let a warmonger have control of the most powerful human nation in Thedas and possibly put the Dalish at risk. So allowing Celene to die, Gaspard to rule, and Briala to rule him in secret was the best option for this Inquisitor. Plus, she had already dealt with the demon army at Adamant, so Celene's death meant nothing by then.
A Vashoth Inquisitor might support Celene, since she seems more likely to keep the Game going, thus supply more opportunities for hired mercs for the nobles. Gaspard might be more focused on building up the Orlesian military, which leaves little room for mercenaries.
Celene and Briala reconciled might benefit the carta in their smuggling, which the dwarven Inquisitor would approve of.
A human warrior might favor Gaspard for his dedication to a strong army to defeat Corypheus, and any hostilities raised between Orlais and Ferelden might benefit the Free Marches since they can sell food and supplies to either side.
So I think the "right" choice depends on your Inquisitor.
Also I read somewhere that you can't use the naked guard's testimony as blackmail against Celene unless your court approval is over 50 or something like that.