Finally got a brialla and celene reunion.

You don't know the inquisition is going to be gone when you make the decision.  Besides to be completely cold about it, it's not my problem.  Gaspard is fundamentally stupid; Celene for all her faults (which are many) is not.  I don't want Orlais to prosper but I do want it hamstrung so a puppet Gaspard is the way to go.  Even if he does eventually shake his chains (by no means a given especially since we know he doesn't as of Trespasser), no one fill forget that he was an Elf's plaything, and thus his potential influence as a political player (even as emperor) will be severely curtained all of which weakens Orlais which IMHO is a good thing.

I have to admit that when you reconcile Celene and Briala the way Briala responds to Celene makes me think that she very much has learned her lesson and that on her side at least it is not genuine affection any more but simply playing her in order to get what she wants. People says that Celene was good at playing the game but I think that is largely down to having Briala at her side as her spymaster. When Briala was away in Halamshiral, Celene made mistake after mistake in not realising that Gaspard was engineering getting her out Val Royeaux and into an area where his supporters were strongest. So from that point of view, Briala is the stronger in the partnership.

I don't like any of the three really. Briala was quite happy to let an entire clan of elves be ripped apart by a demon, when they hadn't actually done her any harm and in fact had saved her entire party from sylvans. She was upset with them because they didn't seem concerned with what happened to city elves when actually they were in no position to do anything even if they were. "They let the elves in the alienages burn because the elves in the alienages were not their people". I doubt the clan were even aware that anything was going on in Halamshiral and even if they did, what could they have done about it? A clan of fifty elves, not all of them combatants. It was Celene who actually burned the elves in the alienage and yet Briala prefers to help Celene at the expense of the clan. Even Gaspard conceded that not even elves deserved what was done to them.

The main reason I like putting Briala in charge is that for a short time at least, the vile nobles have to suck it up and take orders from an elf and they do so because they respect the Inquisition and fear my elven Inquisitor. Briala should also note, he is a Dalish elf who cares about all elves. Nothing you do in Inquisition is lasting but placing Briala on the throne and making Leliana Divine, is probably the best result for the elves, since apparently the Divine does still have influence in these things. Of course, if the nobles are idiots, which they very often are, they will revert to making life difficult for the elves after the Inquisition is gone and thus very effectively drive them into the arms of the Dread Wolf. On the other hand, if they are wise, they will continue to support Briala, because I assume by the end of Trespasser she will have learned that it was Solas who killed her pal, Felassan, and thus she will be determined to work against him.

It is sorta-kinda.  No you can not make her the actual ruler of Orlais, but you can arrange things so that she is the power behind the throne and her puppet (generally Gaspard) can't change his own socks without her approval, Emperor or not.