My daughter who is 9, takes Karate.
Advancement to another belt, is according to the child's competence of their Katas and routines, and if the child has good attendance to class which means dedication to it.
EACH belt color, has a different set of "Kata" or katas, to learn and be competent in. And the child, has to know the Japanese terminology of each Kata.
Some martial arts schools, "promote" the kids, according to real skill... or, according to the kids ALL being promoted so that a kid doesn't feel left out. As you describe your kids' karate school. But, if a child is advanced to another belt color ranking, just so that ALL the kids don't feel left out, it means that the child may or may not be competent in their skills. It does NOT... reflect REAL skill or competence in their Katas or "Kumite" skills.
At my daughter's Karate school, kids are also promoted according to skill and knowledge of their rules and dojo philosophy. And being able to do it.
If a child is not competent in it, they do not advance.
Dojos vary, in how they advance the kids. And it also varies per what type of Marital Art it is.
At my daughter's Karate Dojo, they do not have "testing" or belt promotions, every quarter. It is once or twice a year at most. And in between that, they may be given testing of their skills. Surprise tests.
There are also different degrees, for different belt colors.
My daughter's Karate Dojo, is comprised of many different levels and belts. And of all ages from kids to adults. Students are advanced according to real skill and competence in it.