In reply to Mattyk:
I went to Kendal Wall with my little sister - aged 7, so a bit older. We went to the bouldering area that is set aside for kids, and there was no-one else there, which was great. She was quite excited, but didn't quite see the point of climbing one colour to the top of the wall - and the height scared her. So, my partner and I played a game with her where we hung a red buff around a hold and she had to climb to get to it. Then she got to place the buff, and we would try to get it (with her saying which holds we could use). That worked well.
When we went upstairs, though, where there were adults trying hard on problems, it was quite an intimidating environment for her and I was worried she would step under someone, as excitement + lack of judgement are a tricky combination. Apart from the other people, the bouldering wall was much higher and many of the problems didn't suit her, as the holds were quite far apart relative to her height. We went back downstairs pretty quickly, as I couldn't think of any way of making that room work for her.
I take away from that:
1. It's hard to control the kid whilst keeping the atmosphere light and fun.
2. There's a lot of objective danger where others are climbing.
3. The "games that climbers play" might not appeal to kids, but other games could work well.
4. Rooms/walls where there is child-specific setting are a big bonus.