if you read between the lines, both of them were in fact do realize that it would be futile and ended up as disaster, but they had no choice because, obviously, politics. also, competent doesn't equal to infallible.
Plus, sure, they are competent, but they are just at the right level of competence and ego to assume that while their plan is good, their fellow general isn't (because it isn't what they would do), therefore they must resist to make sure the good plan prevails. And since both do that, the infighting goes even harder for both of them.
General lady’s all “you can’t have 9 other wives“ and yet magically is going to have no problem with Hardlett
Hardlett proves that, in universe, being sufficiently hard lets you get away with a lot of thing.
...... Very high possibility of that happening for real.
Probably not actually taking for wives. But a one time "consoling" them (with his dick), yeah, entirely too likely.