A very excellent point, regarding the qunari. I hadn't considered that.
As for the mountain, well it would come down to whether anyone would see the practicality and be clear headed enough to see the opportunity had. The lannisters might not be so prone to have such a violation of the norm so publicly visible. And I believe brinne was a knight due to the person knighting her and such being a much more open mind on such matters. ((Poor, Poor, Renly. He might have made a good king)).
Renly did think she was ridiculous in private (in the books), but when someone can beat the snot out of Loras in single combat you want them protecting your royal arse.
And apart from the Qunari, Thedas is certainly much less sexist than GRRM's world. Female heads of religion? Empresses with no limit to her power because ladyparts? The equivalent of female Maesters (First Enchanters and scribes)? Women fighters being dime a dozen rather than exceptionally rare? Women in position of power in military organisations like the Seeker, the Templars and the Grey Wardens? That stuff is just not happening in Westeros, just as it almost never happened in real life medieval Europe which both settings are based on. And even then, the Qunari are less sexist than pushing gender roles to the logical extreme, as I see it at least.