Is there any instruction which states that military personnel (specifically males) are not allowed to 'bic' (razor shave) their head?

It would seem inconsistent to have regs that are disposed to resent hair, and also have regs that require hair.
As I once remarked to a buddy with a very high forehead, "I never heard of anyone giged for 'insufficient hair' in any branch of service".

Paragraph 3-2 of AR 670-1 says you may shave your head if you are male. (Last line)

2) Male haircuts. The hair on top of the head must be neatly groomed. The length and bulk of the hair may not be excessive and must present a neat and conservative appearance. The hair must present a tapered appearance. A tapered appearance is one where the outline of the Soldier’s hair conforms to the shape of the head (see scalp line in figure 3–1), curving inward to the natural termination point at the base of the neck. When the hair is combed, it will not fall over the ears or eyebrows, or touch the collar, except for the closely cut hair at the back of the neck. The block-cut fullness in the back is permitted to a moderate degree, as long as the tapered look is maintained. Males are not authorized to wear braids, cornrows, twists, dreadlocks, or locks while in uniform or in civilian clothes on duty. Haircuts with a single, untapered patch of hair on the top of the head (not consistent with natural hair loss) are considered eccentric and are not authorized. Examples include, but are not limited to, when the head is shaved around a strip of hair down the center of the head (mohawk), around a u-shaped hair area (horseshoe), or around a patch of hair on the front top of the head (tear drop). Hair that is completely shaved or trimmed closely to the scalp is authorized. (See figs 3–1 and 3–2.)

Its a personal interpretation. Bald= Faddish.
Had the same nonsense spouted at Flat tops and high and tights..
When I pointed out to those commanders the historical commonness of both cuts (as would be true of baldness as well) they stopped with then nonsense and we focused on more important things that actually effected readiness and the mission.
Id venture to say a SM that shaved their head, and was told no, and then did it again, bought up on charges would find his ability to "wear" his hair in a supported manner by regulation upheld by JAG and the IG, a request for CM by a commander would be tossed...so long as there were no other associated transgression (insubordination, conduct unbecoming, ect and no evidence pointing to the baldness as part of gang or other prohibited group activities)