No where "is it Written" in the Torah that men are "commanded" to cover their heads, either in general living or during times of prayer, minus what is detailed regarding the priestly vestments in Exodus 28:4.
Shulhan Arukh (Jewish Code of Law - mid-16th century), Orach Chayim 2:6: "One may not walk four cubits with an uncovered head."
If one wishes to pay allegiance to the rabbis, then he should do what the rabbis do. If one wishes to pay allegiance to יהוה, then he should do what יהוה said and not add commandments to the Torah (Deuteronomy 12:32).
