There are a lot of great reasons to compete, but the short answer is children should compete because they want to and you believe it will be a positive experience for them (and if it is a positive or not experience isn't necessarily dictated to whether they win or lose). I believe it should be THEIR choice and they'll let you know when they are ready for it. If you push them into this sport too hard, they will wind up hating it later on.

My kids are 13 and 11. They are currently competing in Folk/Freestyle wrestling tournaments and love it! One of my kids made the decision to not play baseball this year to wrestle full time and attend all the tournaments in our association. The other was racing motocross and made the decision to stop racing this year to focus on wrestling and Jiu-Jitsu. They will also be competing in the Celber Jiu-Jitus Tournament on March 11th and 12th with the academy we train with Charles Gracie Academy. Yes, I did ask them what they thought of the idea and they were like "Heck ya, that would be cool". I let my kids make the decisions on what they want to do. My only rule is that they need to do something. I refuse to let them hang out at home doing nothing or hang out on the streets with their friends. All I ask is they try everything at least once. If they don't like it then hey, they don't have to ever do it again. My son's are ok with that. They are doing what they want to do right now. They are the ones that bugged me to get a mat for the house!