Actually, UA actually did conduct their own physicals decades ago requiring among other things different vision standards than the FAA. They got challenged about it and fought it up to the Supreme Court - and won. That lead to Congress eventually changing the Americans with Disabilities Act to prohibit that sort of discrimination.

https://biotech.law.lsu.edu/cphl/articles/sc_ada/mobarada-sutton.html

https://www.eeoc.gov/statutes/ada-amendments-act-2008