I agree. That is the system I am proposing changing.
I understand your desire to assert the 10th Amendment but it would be an additional expense for all states, especially those who do not have a state income tax. They would have to creature and entirely new department and that works against our principles of small government. It would also create endless conflicts and lawsuits with different states withholding money for different reasons.
I like the spirit of your idea but the mechanics need some work.