Why is sexual differentiation necessarily costly in every case? There are many sex differences that give an advantage for one gender that would have been an advantage, or no cost, for the other gender, but weren't as strongly required and so don't exist. Sexual differentiation may be less _likely_ for any given trait, but traits tend to pop up on random chromosomes, or the side effects of sex hormones be farther-reaching than necessary and evolution just "didn't bother to correct," and so I'd expect that some traits that don't necessarily need to be dimorphic (but are needed by one gender or the other) might become dimorphic just by chance.

Men have deeper voices than women. What would be the disadvantage for baritone women? You could argue that a deeper voice makes you less easily heard by prey... but then what's the advantage for women to have a higher pitched voice? Why didn't we all continue this trend to speak at the registry of blue whales? I suspect it's one of those things that "just sort of happened" and then it became a positive feedback loop spurred on by sexual attraction as a result of this initial differentiation, and now we're just at a pretty good state spurred on by a combination of random chance, survival advantage, and a little reproductive enforcement.

Increased sexual dimorphism (and a genetic/hormonal configuration that lowers the cost and increases the odds of sexual dimorphism happening for any given feature) is actually a positive thing for some animals depending on their social and reproductive strategies. When sexual dimorphism is high, you tend to see more random differences that pop up between the sexes but that may or may not provide any evolutionary advantage beyond "well, the other sex is just attracted to it now so let's keep this party going." When dimorphism is low, differences generally have to provide a stronger survival advantage.

Evolution isn't always straightforward or "carefully thought out." The hoops it jumps through aren't always costly and don't always have a rhyme or reason. It's often chaotic and and takes weird turns and it's not like humans are at a "final state" anyway. We're evolving.

I'm not _necessarily_ disagreeing with you (although it's probably ultimately easier to look at the physics, not biology, to prove or disprove your point) but I'm just saying that I think the situation is vastly more complicated than "sexual differences are costly." I don't think they're necessarily costly, simply less likely. A subtle, but important difference.