My Daughter takes Karate. And my son is also interested although he is too young.
Martial arts is great. It teaches discipline, respect, and how to handle your body control, and builds self-confidence and self-awareness etc. IF the Teacher is good, and teaches proper rules.
It is not about how "tough" a kid is. But rather, often the "toughest" and best Martial artist will also be the humblest.
It takes consistency, like anything else, to learn it. AND, children are taught that they must NOT use their self-defense skills outside of their Marital arts school, and it is NOT to be used at school against other kids. Of course, if the child is somewhere else or is in real trouble, then that is another story.
My daughter loves it. Granted, it is not easy and the Teacher can be strict, but she enjoys it very much.
It does build physical fitness as well. Which is good.
For me as a Mom, I am just glad that my daughter enjoys her lessons AND that in the future if need be as a young girl/woman, she will be able to defend herself and be confident in doing so... and it has strengthened her sense of self too. A proper Martial Arts Teacher... WILL teach children proper rules of conduct, and they will not focus on bad attitudes nor tolerate it.
As for cost, it can be costly. BUT... try your local YMCA. The one's in my city teaches a variety of martial arts, taught by VERY high ranking volunteers. Or, try other community programs. Not all martial arts schools will cost a lot. Some are not. But always observe a class... and talk with the instructor first, before deciding on one and paying.
All the best,
Susan