Are you the 13 year old in question? Or the parent? Anyways, I do not think that's a good idea. It could send the wrong message. A lot of 13 year olds are more mature than they need to be anyway! Be a kid. Plus, you could break your ankle!
honestly i wouldn't mind if it was for one day out of the month or something it would be quite ridiculess but if they really wanted to i would let them but i would never let them use them more then a couple days a month or something because there really bad for your back and stuff but i would surely let them try new things :) hope this helps
I think one shouldn't wear it that high, but they could always wear one inch ones (way 2 young). Or they could always do 2 inch high wedges, they don't look as inapropriate and people can actually walk in them!