In the United States, my understanding is that your medical & employment discrimination scenarios are already illegal due to the Genetic Information Nondiscrimination Act of 2008.
There was already an effort to weaken this law in 2017. It didn’t pass, but if corporations are lobbying for loopholes it would be entirely unsurprising to see some slip into future legislation. https://www.vox.com/policy-and-politics/2017/3/13/14907250/h...
Any law could be subverted via these justifications. "Why should I register my gun when the government itself breaks laws, and its politicians corrupted by bribes!"
They'll get sued immediately by everyone who is denied a job following a genetic screen.
There's a reason companies who require a physical or medical history (usually done to find pre existing conditions to protect against future workman's comp claims) do it after the job offer has been extended (it's risky to rescind an offer for no reason by the way) - if they did it before, every applicant with a disability (and their pro-bono lawyers taking a slam dunk case) who did not get the job would sue.
Or bribed politicians to change them?