I've done it - it's not all that bad other than having to deal with the throngs of timid idiots who get halfway up and then freak out or just stand there, log-jamming the ascent for the 200 people behind them.
A 13 y/o is a judgment call. If they're responsible and have a healthy respect for things that could hurt or kill them I'd say sure - it's a great experience. On the other hand if they suffer from teenage "I-think-I'm-immortal-and-can-do-anything" syndrome, you might rethink it.
On my last time up there I was stuck in traffic and a guy two people in front of me turned around to ask his GF if she could retrieve a water bottle from her pack because she was thirsty. She reached in and got it but it slipped out of her hands and started rocketing down the slope. Instinctively she let go of the cable and turned to try and grab it before it got away and started to lose her balance. I had to grab her and physically throw her back onto the cable so she didn't end up sliding down to who-knows-where herself. Very weird and awkward moment (especially because I didn't know her) but she had eyes as big as dinner plates afterwards was a bit shaken realizing what almost happened and just said "thanks, sorry about that". My point is that it's a "routine" climb and a lot of people do it, but that doesn't mean it's not potentially dangerous. There are a lot of stupid people in the world and its frustrating when you're in a situation where they can create a real danger to themselves or others.
Go have fun, be careful and enjoy it at the top. Wear boots with good soles.
