If the State can show that students of a Yeshiva are not self-sufficient and rely on social programs, the Yeshiva will not be able to make a strong case based on Yoder. The State does not need to show why they are impoverished, just that a disproportionate are.
This isn’t so difficult. If the reason for “impoverishment” isn’t lack of education or lower gross income, it makes no sense to address it by changing educational standards.