What is the big deal? The Reading obviously does not say that any woman must cover her hair, but gives some commandments and guidelines to muminati:
24:31 Tell the muminati to lower their gaze and guard their private parts, and that they should not show off their attraction except what is apparent, and let them cast their clothes over their cleavage. Let them not show off their attraction except to their husbands, or their fathers, or fathers of their husbands, or their sons, or the sons of their husbands, or their brothers, or the sons of their brothers, or the sons of their sisters, or their children that come after them, or those who are still their dependants, or the male servants who are without need, or the child who has not yet understood the nakedness of women. Let them not strike with their feet in a manner that reveals what they are keeping hidden of their attraction. Repent to God, all of you acknowledgers, so that you may succeed.
33:59 O Prophet! Tell your wives, your daughters, and the women of the mumineen that they should draw down over them some of their outer garments. That is better so that they would be recognized and not harmed. God is Absolver of imperfections, Merciful.
If a woman wants to cover her hair, what or who's to stop her? Also, these commandments are not to be imposed - non-believers in a true mumin society could reasonably wear slightly more lax clothing. As long as there is no half-nakedness like today it should be fine.
What do I think is a minimum modest dress for muminati? A skirt/dress that comfortably goes past the knees while seated, shoulders down to legs completely covered - both front and back, regular shoes - no high heels, flip-flops or ballerinas. In my opinion, neck, face, forearms, hands and lower part of legs can be shown. Moderaely modest would be to only show neck, face and hands. Very modest would be to also wear a head cover. Also, wearing tight or see-through clothing and excessive make-up defeats the purpose of covering. I dont think a head cover is at all necessary, but is certainly to be left for personal choice.
The God knows best the way he designed men. That is why men, like women, should lower their gaze, but that is not enough. Muminati should observe a modest dress code. That way, especialy in today's society (in the West) in which most females dress immodestly in warm months and many outright dress like sluts, you would be distinguishing yourself from other women and get less attention from men.