Anyone who has been around kids, who has been a parent or a coach or a teacher, knows intuitively that applying themselves to something... anything... can result in the development of self discipline, self esteem, self-awareness and a strong work ethic. These are part and parcel to learning how to do something well. But it's not unique to martial arts, and I would argue that kids' martial arts programs focusing on the development of these things can miss the forest for the trees and actually DON'T provide these things as well as, say, learning to play the flute.
To suggest the martial arts do a BETTER job of teaching kids values than, say, playing soccer or participating on the debate team or the chess team or learning to play the violin is bogus. In my opinion, learning an activity and applying oneself is where the character development comes from. I'd also add that a mcdojo, where the kids are rewarded for nothing, is doing the child a disservice. When the bubble bursts, you will have created for that child a crisis of confidence.
I personally believe that sporting martial arts (or said another way, martial arts with a competitive element) are better for children than self defense oriented arts for self development. The reason I believe this is that children learn best by doing. People in general do. So, if you want to teach a kid to cook, you cook with the kid. If you want to teach a child to play football, you play football with the child. They learn to play the flute by actually playing the flute.
But for some reason, many Martial Arts operate under a completely different learning model. You don't learn by doing. I don't want to get into a kata vs sparring whatever discussion. That's not my intent. I'm speaking specifically to the stated "benefits" of martial arts, and my belief that the feedback that kids get from competition is extremely beneficial. So many life lessons can be learned in a positive, competitive environment. Giving kids a chance to kick each other. To use their skills, but also to be a good sport, control their emotions and their adrenaline, to learn how it feels to win and how to lose with grace. These things don't just happen. Competitions also help a child set realistic short term and long term goal setting.
All of these benefits are, I believe, lacking in many non-competitive programs. I don't believe that these things are learned by kids when they train in a style that offers no competitive outlet. Personally, if given the choice for a child, I'd pick a TKD school that actively participates in competition over a school that does not.