This is a good question!
My DS knows that he is profoundly gifted because of all the educational issues we've encountered, but we have not let him see his actual scores. Of course, he just turned 6, but I don't foresee sharing them anytime in the foreseeable future.
My parents never told me. When my husband disclosed his one day and I called my mom, I was shocked. I was well aware that I was intelligent, but had no idea where I was in the gifted spectrum. (I just assumed gifted was gifted.) I completely understand why there was no need to share it with me as a child, though.
I guess my opinion is that IQ is nobody's business (like a woman's weight!), and except for assisting our children's educational needs, it usually only leads to judgment and division. Nearly everyone the child encounters will have a number higher or lower. The ones who are higher will assume your child is less smart than them, and the ones who are lower might be competitive/jealous/etc. I'm not sure the numbers have a good use in a child's hands.
After reading many testing posts here, I also see that the numbers can sometimes be off. Perhaps the child had a bad testing day or some other variable occurred, and the numbers are really higher. I also wouldn't want my preteen/teen googling the stereotypes about various gifted levels and worrying about some of the more troublesome aspects that are often listed, particularly at the higher levels.
It's such an interesting question, though. I haven't pondered it before, but there are great thoughts pro and con.
