Read the passage again. If the hair were meant to be the covering of the head,
1 cor 11
14 Doth not even nature itself teach you, that, if a man have long hair, it is a shame unto him?
15 But if a woman have long hair, it is a glory to her: for her hair is given her for a covering.
I believe you are confounding the meaning of covering in verses 14 and 15 with that in the earlier verses.
In the earlier verses, the word translated in the AV as “covering” is from the Greek root “katakalupto”, which is an article of clothing that hangs down.
In verses 14 and 15, the word translated as “covering” in the AV is from the Greek root “peribolaiou”, which signifies a garment that is cast around, in this case, the shoulders.
And the earlier verses would not make sense if you replace the word “cover” with the word “hair”. It is a shame for a man to pray with hair on his head, and if a woman pray without hair, let her hair be cut.
And we have almost 2000 years of church history where the sense of these verses was clearly interpreted to mean some kind of head covering for the woman, be it a bonnet or kerchief.
About 150 years ago, women started wearing absurd hats as coverings in church, some looking like caricatures of mens’ hats, and others having what appeared to be birds’ nests and baskets of fruit.
Perhaps the preachers were relieved when women stopped wearing coverings at all, in the last 50 or so years.