Interesting points. But I would add that sexual selection can select for some trait that is actually counterproductive, a famous example being peacock tails. Female peacocks use them to evaluate the health of potential partners, so it is an indirect measure of fitness to the environment. But at the same time, it is clear that healthy peacocks would still be better off without carrying around such big tails. If tails weren't so important for reproduction, they would have likely shrunk by now. I wonder how a comparison with the methods you mentioned would capture this.