Importantly, the lever the feds you is the school lunch program. And for decades they have demanded that schools must follow their rules or be cut off from the lunch program.
However, there are now hundreds of requirements all threatening the same thing, so states are seriously considering allowing school districts to opt out of the federal program, if they can provide their own program at greater efficiency, that is, lower cost and more meals served.
This makes sense, if say, the feds offer $1 per student per day, but demand $3 per student per day back in unrelated compliance costs. If the school can raise $1.50 per student per day, they can actually save lots of money by canceling all the other federal demands.
When Caesar feeds you, you will eat what Caesar gives you. And you'll do whatever else Caesar wants you to do, too ... even if it means bending over and kissing your own @ss.