A clean-shaven head is not the norm in the US military. Closely cropped hair is, and in basic training we were given a large number of partially conflicting reasons for this. Hygiene is often cited, as lice on campaign has historically been a huge problem for soldiers. The IET Soldier's Handbook still (as of 2004, when I went in and God I'm old now) still detailed several methods to treat clothes to prevent various infestations of insects. Closely cropped hair is easier to maintain and to keep free of lice and other insects that carry infectious diseases.

We also are told that it is a necessity to form a good seal on our gas masks, as excessive hair could prevent that from happening--especially facial hair. Because of this, the standard became (again, according to various drill sergeants and military manuals we had to read during basic training) shorter hair. IIRC, this is also reiterated in the IET Soldier's Handbook, but it's been over a decade since I read mine, so it may have just been what we got repeated to us by numerous people during our training.

If I were to offer a speculative answer, it would be that Sergeant Major Hardass made his men do it, the other sergeants major saw it and got jealous, and then suddenly it became a standard because it gave some crusty senior enlisted who had nothing else to do with his time than make the lives of junior enlisted miserable a raging boner. But that's just cynicism speaking, and speculative answers are not allowed on this sub. So stick with the first two.