The head covering (or veil) that Paul was talking about in
I Corinthians 11 was a first century standard of modesty for women.
Any time a woman covers herself in modesty, she reveals that she is submitted to authority and honors her head (meaning her husband).
1 Corinthians 11:3
But I would have you know, that the head of every man is Christ; and the head of the woman is the man; and the head of Christ is God.
An immodest and shameful woman is clearly not in submission. And she dishonors her head (meaning husband). Appearing immodest in public, or in worship gatherings, is just as shameful to her husband as it would be if she were publically put to shame like a prostitute (which involved the shaving or sheering of the hair).
1 Corinthians 11:5 (KJV)
5 But every woman that prayeth or prophesieth with her head uncovered dishonoureth her head: for that is even all one as if she were shaven.
The entire issue isn't about holy magic hair, uncut hair, or having authority over angels or spirits. It's about submission, modesty, and honoring one's husband by wearing modest attire.