I own a footwear store and this story makes me sad and angry.  

The idea that women have to go through physical agony during the day is ridiculous.  I can see someone being physically exhausted if they need to lift or move items all day.  High heel shoes  in a professional setting, however, serve no useful purpose.   I have nothing against heels.  Love them, own them and sell them.
However, when I am on my feet for more than 2 hours, I wear shoes that have comfort features.  Sometimes a lower heel helps comfort and/ or the material and quality of the shoe.  The insole properties. The shape of the instep and toe of the shoe etc.  
There are many great shoe brands that look gorgeous at work.  Some have a lower heels and look great.

The rules should, of course, be the same for males and females in a work place.  If it is a professional setting, it might be that the shoes must be tidy, clean and not sneakers or sandals.  Whatever the rule, it should increase comfort and productivity.