Look at the big picture. Her pro-elven disposition was bleeding her support. The more support she lost, the easier it would be for Gaspard to succeed in his attempts to usurp her. Briala's solution (Actually I think it was Celene's idea) was intended to quiet that one revolution. Burning Halamshiral was intended to stop Gaspard from launching one: a show of force to quiet the rumors and strengthen her authority, to stop a destructive war and protect all she's done to drag Orlais kicking and screaming into a new more egalitarian era. It wasn't because of the play.
The play was sponsored by Remache. Seeing it just showed Celene Gaspard's newest tactic in destabilizing her rule. And that it was working. What Leliana told her about what University scholars were doing to defame elves only confirmed it. The Divine told Celene the situation needed to be dealt with if stability was to be maintained. The play was nothing but a sympton, to call it the cause of the attack is to oversimplify a very complicated situation.
The big picture is that Celene had two paths to choose from: taking direct action against the elves or take indirect action. At the beginning she chose the second, then, after the play, she chose the first. Of course, both had advantages and disadvantages. No one has the benefit of claiming "this is the pragmatic option". Especially for one big reason: because we do know that the correct option was to wait, since it was a trap set by Gaspard. And Celene hasn't even the option to say "no one could have seen that coming", because Briala saw it coming (ch7).
That any other similar event could have sparked it is both true and inconsequential, since Celene wasn't forced into action by things that didn't happen, but by a play that did happen. In the end, the only people who were punished because of the play were the elves. Remache met his end because of another reason. And that's the sadness of it.
Ahh but what Briala is using the eluvians to attack supply lines? Send assassins into meeting? You've convinced Gaspard to force march his men to the defence of an Inquisition fortress about to be over run by demons and Briala choose this moment to attack Verchiel?
Briala's stated intention is to prolong the war and weaken the humans. For the inquisitor who's goal is to unite, defend and eventually close a veil tear, her goals as we know to this point sound to be against ours.
I agree it will be interesting to play out, siding with the various factions which I fully intend to explore. But in the hypothetical, gun to your head, pick one of your wardens, one of your hawkes and this is your world state (not sure about you, but I do have a 'main' warden and hawke I plan to recreate in the keep), I'm not sure I would be playing an Inquisitor that actively supported the elves.
If Briala becomes an obstacle, she will end up badly. Frankly, I didn't expect any elven side to put anything of value on the table for the Inquisition.
BUT control of the Eluvians is a major thing. For an organization such as the Inquisition, taking control of a vast network of fast travel in Thedas would be as good as having one of the contender's armies. Briala can negotiate since it isn't as easy as "you killed it, you bought it"; without the password, the Eluvians are almost useless.