Just because it's cliche doesn't mean it actually works. It's true that there are many reasons Diana and Bruce are fundamentally incompatible, and his bigotry is merely one of them. Nevertheless, his bigotry is very much one of them, and it is not romantic to give her the responsibility of putting up with his prejudice or trying (fruitlessly) to educate him out of it in a relationship that should be a source of strength and support for her, not further work and stress. (Interestingly, Bruce's muggle-centric issues don't conflict with the Clark/Bruce pairing - not just because his hatred of metas is less than that of magic, as metas can be basically understood, but because Clark himself is ashamed of his powers on some level and to some degree - at the very least he's no less concerned by them, which has probably a lot to do with why Bruce is able to be so comfortable with him).
The other thing is, while obviously editorial sexual mores play a part, I think even without them you'd still have the problem, because I don't think Bruce, as a character, could ever be comfortable interacting with Diana that way. Selina, yes, Talia, yes; they're Bad Girls who use sex as a deception or like a weapon, and Bruce is comfortable with weapons and deceit. Sex as a toy, shared by two friends, would freak his ass right out and I can't see him not seeing it as disrespectful to the woman he's with.
I like your plane scenario, though. Too much of a critique to ever fly, and elevates the amazons morally far more than DC right now could ever stomach, but still a pleasant thought.