Actually, I think you are most correct on the bad ass bit and I would argue (and have) that one of the reaons Leia was generally forgotten for decades was that Buffy, Katniss, Hermione, etc. are bad ass without the firearm.

But yes, the general point remains. We think of women as better leaders because they are more reasonable, less prone to succumbing to “toxic masculinity,” but then cheer when they draw the sword or throw the punch.