God bless you. You are absolutely right.
Covering head and hair has nothing to do with Islam. It is OK for woman to pray and to work and to travel without covering her head. In Ablution before prayer we wash what is usually uncovered like face, head, hair,.etc.
Verse( 24 : 31 )talks only in covering the Chest of woman (Al Khemar )not her head.
This Hijab is something that they need to have themselves distinguished in their Diaspora, giving them the feel of being different and being better than others.