It’s great that people find that veils and hats on women in church remind them to be devout and humble. But that’s not why it’s done.
It’s not because no Jewish woman would visit the Temple without her head covered, and it’s not because the tabernacle is veiled.
It’s because no decent woman of the ancient world – Jewish, Roman, or most other cultures – would go out in public without her head covered. They didn’t wear headcoverings indoors with friends and family, and so they started not wearing them indoors with the ecclesia, their brothers and sisters. St. Paul told them nope. His reasoning was that the angels are there in church, too, and they’re not so much our brothers and sisters; you’re still in public, so keep your stola on. You will note that the surrounding verses are also about decorum and formality being maintained in church.
So you can take it as a sign of humility and devotion, of course. But primarily, it’s a sign of formality, and that church is a public place.