Whether it is psychological or traditional in nature, I think there is a couple interesting things to consider about veiling. First, when women were ordered to unveil in 1936 it was education that won the day. Women's opportunities in academics help to facilitate the radical change. When the ignorant become educated they naturally help to facilitate change. For example, when the king publicly introduced his female family members it was educated women who cheered.
Education is always the key to change.
Secondly, the whole concept of religion dominating society is antiquated and absurd. When Khomeini assumed power he began to re-institute the rule of veiling women. The founders of this country recognized the dangers of having the Church rule the State. Our country sought to deny religion's domination by creating a separation of Church and State. As a result many immigrants had come to this country to escape repressive religious rule.