Some jobs require certain dress codes.
In a customer facing role employers will expect employees to dress professionally. It seems we all have a different view of what is professional. In some sectors, alongside smart suits, employers consider make up and heels an important part of a professional look. Of course employees should dress smartly if the job requires them to present a professional image. But if a boss would not ask a man to be clean shaven, I think there are issues around asking a woman to wear high heels. Flat shoes can be smart and professional too.
Some shoes are inappropriate for an office environment and its quite right for employers to be able to say no trainers, no flip flops, no slippers. In some workplaces high heels are not appropriate and hard boots are required.