Madonna's Daughter Shaves Her Head

Madonna’s 15-year-old daughter Lourdes Leon was spotted recently with a drastically different hairstyle. Sporting a bun on the top of her head, the sides were shaved.
And Lourdes isn’t the only celebrity offspring that has recently shaved her head. Willow Smith, the 11-year-old daughter of Will Smith and Jada Pinkett-Smith, recently shaved her entire head. The Whip My Hair singer will no longer have any hair to whip back and forth.
So, this brings a question to my mind: should children be allowed to style their hair however they want?
I still have young kids who really have no say in their hair style. My boys get their hair cut regularly, and my daughter has only ever had a trim. As they get older, I will allow some leeway with their hair styles; but I am not sure I would allow my daughter to ever shave her head - or allow my sons to grow their hair long enough to look feminine. I guess, to me, my kids are a reflection of myself until they are adults. Because I have a rather conservative style, my kids will have the same style while I am still paying for their haircuts and clothes.

Would you let your daughter shave her head? Do your kids get to choose their hairstyles?