With any society-wide standards we have some centralized group with expertise in that area. Depts of transportation, for safety standards on the roads. Depts of health, for public health issues. Depts of education, for standards of education. The Board of Education allows and encourages input from parents and others.
I don't know that there have been any studies directly comparing public school graduates to graduates of yeshivas that have no secular education.
But the state can decide to intervene if a parent provides less nutrition or less health care than the state claims is necessary. You have a lot of leeway, but still need to meet certain minimal standards.
1) IINM, one of the aspects of these regulations is that anyone can lodge a complaint, not necessarily the BOE, a parent or a student. Anyone.
2) I have the right to be as unhealthy as I want or drive any vehicle any way on my ranch. I can't when it affects you. If you want to so drastically curtail the rights of so many thousands of religious citizens, sure the BOE should be able to point at their vigorous studies that show that yeshivah graduates are placing an undue burden on society more than their counterparts who graduated public school with the minimum standards proposed. They can't and won't be able to do that because it is simply not true by any measure.
Yes, the government can intervene if my child is undernourished, but they cannot if they don't approve of the diet I use to achieve proper nourishment. And the numerous hair raising stories of CPS taking children away from parents based on no evidence at all of wrongdoing are a chilling reminder that we ought to think twice, three times, and then another 50 times before giving government any power to intervene on children's behalf.