Divine Justinia's "neutrality" is a joke.

It's right. Just like she knew about Alrik's "tranquil solution", and yes, she rejected that – but was not suspicious what happened there? Doesn't send away that obviously mad man from the Order? She watched Kirkwall – but just because of the blood mage and the Resolutionst's activity, and because of a possible mage rebellion. Not because of among her Templars there are madmen. Even Cassandra said, they made the mistake, they did not pay attention to Meredith.

And ... Leliana in the Masqued Empire:
“I have… been comrade-in-arms with elves. I would not see them harmed. But you did not ask for her support in that matter.” She looked back at Celene. “You asked for her support calming the Templars and the mages.”
“Indeed.” Celene nodded. “And will she give that support?”
Leliana let out a breath. “She will,” she said, nodding slowly, “but in return, she needs to know that this matter with the elves is under control.”

Divine Justinia seems even didn't care about the elves – she just wanted under control them, don't care about the method... She just was a politician. Probably not the worst, but not even the best one. Not a big loss.

And in Asunder, she agreed with Lord Seeker Lucius to Tranquilizing Pharamond again.

I'm not sure it was a retcon. They might have been planning to write her as somewhat biased toward mages the whole time, but have already decided that the problem-templars would have been able to keep things hidden from her. (Which is how they explain the discrepancy in later media.)

She does send her Left Hand on a factfinding mission, right? As though she doesn't really trust the official word on things. And then that Left Hand discovers that the mages in Kirkwall really are running amok, and leaves quickly since they find her and attack her. And then theDivine sends her Right and Left Hands on another factfinding mission after the powder keg bursts, just to be sure she has the whole story.

I remember reading something on TV Tropes that said the Warden was Divine Justinia's first choice to lead it, and that reminds us of all the violence and hardball politics the Warden had employ even if you're playing as the most gentle Warden the game allows. I can't find that original post anymore, so maybe it's gotten taken down, but if the Divine really did plan to put the Warden in charge of restoring order, that does give us some hint as to how she thought it would have to happen.

We'll ignore all the darkspawn you have to kill, since they're narratively crafted in such a way as to not count, but have you ever managed to roll a Warden who killed more darkspawn than people? Have you ever rolled a Warden who got through A Paragon of Her Kind without either Bhelen or Harrowmont dying? Who got through the Landsmeet without having to kill at least one important nobleman? Have you ever managed to roll a Warden-Commander who shut down Bann Esmerelle without resorting to either violence or the threat of violence?

I'd say that if Divine Justinia really wanted the Warden to run the Inquisition, she figured she'd need some eggs broken if she wanted to make an omelette.

Not just TV Tropes. Cassandra says it herself.

First in DA 2's ending, when Leliana asks where is the Champion and she answers "Gone, just like the Warden (meaning they looked for him/her first). And again, in a conversation with Cassandra in Inquisition.