Everything you say makes sense, but it does not describe the sort of idle animation that a lot of 2d games are plagued with. I don't like tradition as an end in itself and I feel the generic idle bouncy animation for fighter sprites should be evaluated with a bit more critical thinking than it usually is. What you're describing would take a complex animation system to be rendered but it would be worth it much more than the generic 2 pixel vertical bounce.
Well, I think a little bouncing is better than just standing there. Sure, more realistic animations would be great, but there are other factors to consider. Aside from development time, there's the gameplay fact that realistic "idle" animation would involve moving the character forward and back, and players won't like it if their character is moving without their control.
I think the problem isn't with the nature of the motion, since bobbing and weaving is one of the things that boxers do when they're not actively throwing a punch or blocking one, but rather just that the character is only doing one thing. The bobbing and weaving should be continuous, as it is now, but preferably with some rotation of the upper torso and/or "leaning" to the character's left and right, i.e. towards and away from the viewer. Also, the head should be moving around more, as that's the target you really want to make hard to hit. Finally, some other "feinting" should be thrown in... move the left hand a little forward once in a while, or twist the right shoulder slightly forward, as if starting to throw a jab or right cross. I guess you'd have to do the character as more than a single image, so that you could superimpose e.g. an arm animation or a duck of the head on top of the constant bobbing.