I would note that through much of the time right up to the 20th century when women wore head coverings in the church, the head coverings did not necessarily have to be the veil that most women choose today, but could also just be a hat or cap of the type normally worn by women in whatever area of the world they were in.
Many societies, including Western Europe and North America, expected women to wear a hat or cap of some type whenever they were outside their home. Right up to about WWII, women did not go out shopping or to an office job or to do any sort of errand beyond just visiting the neighbor, without having some type of hat on. The style of hats varied a lot over time with the fashion and the age/ culture of the wearer, but some type of hat was essential, so a woman would be wearing her hat to church the same way as she would be wearing it out to lunch, or out to the department store. She could have a special hat or special veil for church, but many women didn’t have anything special and just wore their regular nice dressy hat.
The Vatican removal of the requirement for head coverings happened about the same time that the fashions in the west no longer required women to have a hat on when they went out in public.