Cassandra is no more objective than Leliana. Anything and everything based on faith is subjective, and basing something on Chantry doctrine is no more logically salient than following your intuition if it's not based on empirical observation. For instance, I'm fairly sure there's no empirical evidence that men are incapable of being spiritual leaders, or elves, for that matter.
While we can't have specific theological talks with them like we can with Mother Giselle, Cass is repeatedly shown to care about the truth, no matter how it makes her feel. Leliana is the opposite, it's always been about happy feelings for her.
Aside from the fact that no Divine has any templars initially if you play In Hushed Whispers, there's nothing at all preventing Leliana from just gathering more people to be the Chantry's army if she needs them.
Leliana specifically doesn't want an armed Chantry, though. She might change her mind later, of course, if she realized it was absolutely needed.
Now, I think some of the reforms from Leliana and Cassandra can work. The Chantry is not as monolithic as we're sometimes lead to believe, and neither is the Chant. The highly political way it was shaped is apparently well-known to at least clerics and scholars, as are the Dissonant Verses despite the fact that they're not supposed to be known. I think one of the biggest problems that a reform-minded new Divine will initially face is the fact that many of the progressive, scholarly, peace-minded ranking members of the clergy probably blew up with the Conclave. Anyone who might have had Justinia's favor was there, at least, unless they decided to decline like Mother Giselle did in order to help the refugees instead. Still, both Leliana and Cassandra can get elected and do all right, so they have support somewhere.
As for the female-only priesthood, that always struck me as a bit odd. RL-religions which ban women from becoming priests have sexist doctrines and come from sexist societies in which men have all the power anyway. Andrastianism is not anti-men and Thedas is not matriarchal. Yes, I know, Maferath. But the stories of Andraste also have plenty of positive male figures: Shartan (for all the good it did him later), Hector (who died trying to defend Andraste when she was captured), Havard (who gathered her Ashes and carried them home to Ferelden). Hessarian is the model of the repentant sinner, and his "Sword of Mercy" is an important Chantry symbol. So the all-female clergy feels like hamfisting a reverse-Christanity-aspect more than a trait based on in-world logic.
The problem with re-canonizing Shartan and opening the priesthood to elves, on the other hand, is that there's an elf running around all bent on annihilating the whole world.
And it looks like quite a few elves are disappearing and potentially trying to join him, despite the fact that they're not the "real elves" he's doing it for. That isn't going to make Thedas a friendlier place for elves.