1 Corinthians 11:4 Every man praying or prophesying, having his head covered, dishonoureth his head.

You seem to be off when you think that the whole thing is about heads with hair. You need to take into consideration 1 Corinthians 11:3 before you conclude that it is all about hair covering a head.

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.

I do not think that the covering and uncovering of these heads is hair and hats. Read the section over knowing who the heads that are being discussed are and tell me if it is as simple as long hair and hats.