The Zohar does not say to cut the hair, it just talks about not showing it. They cut it to make sure it does not show. Before the advent of the fancy sheitels female shaving was a problem of making the wife unappealing in the eyes of her husband.
Chazizah for tefilin? Please, learn Hilchos Chatzizos in Y.D.198, you’ll see it is not really a problem.