Wouldn't that just drive the already risk averse mindset in to overdrive, if you have to justify why you didn't hire someone and prove it? If the hiring pool is by law a potential mine field of lawsuits, actual hiring would be even more of an obfuscated process of who you know that is connected to the powers that be, so it can sidestep all the nonsense.
Also.....imagine the scenario where you have three candidates, all equally qualified for a position. All are smart, hygienic, reasonably attractive, snappy dressers and positive, pleasant people (at least in the interview.) All the same gender. Let's just make them all the same minority race too, just to eliminate that variable.
One of them is rail thin. One of them is easily 150 pounds overweight. One of them is 9% body fat and clearly works out seriously, has lots of muscle.
You're going to the hire the fitter person, pretty much no matter the job. That's just kind of human nature. By dint of their physique, you already know that candidate #3 has a strong work ethic and is willing to go the distance to achieve what they want, and the simple fact that they're more aesthetically pleasing on average to the other candidates makes them more appealing.
What are you gonna tell candidates #1 and #2? Either or is "body shaming" on some level, and the argument would be made by someone that they've been discriminated against. If you clearly explain that the only difference between them were their bodies and that made the decision, no one would accept that despite it being the truth. They would ask "why do our bodies have anything to do with a job not involving your physical appearance."
Regardless of how much employers are going to pay, and how much they have the labor market by the nuts, hiring is still mostly a meritocracy. Which in theory is a good thing because it's a motivation to be better than other applicants. I'm not saying I would love reform across the whole area, but putting hiring practices under a microscope I don't think would have the pay off you desire.