Two things: the training itself, and their parents.
Typically, a martial arts student learns discipline, commitment, and a strong work ethic. That can be built in other ways, yes. School sports, after-school programs, strict parenting, etc. But not everyone gets those, either. Lots of kids have very little direction. They go to school, then go home and goof off all day. I'd argue that's more and more kids nowadays, since teachers have less authority and parents seem more interested in being their kids friends than being their parents.
That's the other thing: the parents. I've heard so many horror stories of school teachers (regular school, not martial arts school) who have parents coming down and complaining if their kid gets in trouble or gets a bad grade. And the parents complain loud enough to whatever higher authority will listen, and the teacher has to give the kid an A or take away their detention, even though the poor grade or the punishment was earned. That doesn't happen at my Taekwondo school. If anything, the parents are more likely to complain that we're being too lenient on their kids, or not pushing their kids hard enough!
All of our children students are their because their parents want them to learn at least one of confidence, discipline, diligence, or self-defense. Or, at the very least, they want their kid to get exercise or have something to set them apart on their college applications later in life. Or it could be something the kid wants to do, or something the parent wants to do with the kid. All of these cases have one thing in common: the parents are actively invested in their kids lives. And kids with invested parents tend to excel.