Unfortunately there are many frum kids in Public School because parents can’t afford Yeshiva tuition and they had to make that decision to survive. It is very sad but that is the unhappy truth. Kids are thrown out of yeshivas if the parents don’t pay tuition and there are no alternatives, kids have to go to school.
B”H in my community the Rabbonim really work hard together to try and make sure that every kid is in one of the yeshivas. It is a daunting task and a community effort. But it doesn’t always work. People always ask why are tuitions so high, it can’t possibly cost that much to educate a child. It doesn’t. Those who pay full tuition are paying for their child and a padding to cover expenses for scholarships for others. It is a formula worked out for these purposes.