No, there were plenty of cases in the control group, it's just that there were zero cases in the experimental group. So they know it's very effective, but they were unable to measure the breakthrough infection rate.
How many cases in the control group are we talking about when there were only about 1,100 kids in it?
Also, why is it believed that the vaccine is "very effective" against breakthrough infection in children when that is not the case for other age groups, where the story is "doesn't prevent infection but it works against severe illness"?
18 cases. I'm not sure I understand your point about breakthrough infections in other groups; do you mean that a significant percentage of vaccinated individuals are getting infected, compared to unvaccinated individuals?
Enough vaccinated individuals are being infected for the CDC to conclude in the Provincetown study that "the vaccinated may spread the Delta variant as easily as the unvaccinated." Any time a breakthrough case is reported now you can consistently find statements from public health officials saying "the vaccines don't necessarily keep you from getting sick but they are still effective against hospitalization and death." Given that they don't do routine testing of trial subjects, we can't really even conclude anything from "18 cases in the control group and none in the experimental" except that the vaccines are suppressing symptoms of illness.
Second the other child comment's request for a source on "18 cases," the only thing I can find in the Pfizer press release and major media sources on this is statements about antibody levels.
Also, why is it believed that the vaccine is "very effective" against breakthrough infection in children when that is not the case for other age groups, where the story is "doesn't prevent infection but it works against severe illness"?