That's a good question Oliviaforever. And the answer is that it doesn't.
In fact, the Supreme Court has officially clarified that the Constitution's silence about any issue, school lunches for intrastate schools in this example, means that the federal government is prohibited from interefering with such things.
”From the accepted doctrine that the United States is a government of delegated powers, it follows that those not expressly granted, or reasonably to be implied from such as are conferred, are reserved to the states, or to the people. To forestall any suggestion to the contrary, the Tenth Amendment was adopted. The same proposition, otherwise stated, is that powers not granted are prohibited [emphasis added].” —United States v. Butler, 1936.
SCOTUS underwent a pretty sharp change since US v. Butler in 1936. See Wickard v. Filburn, 317 U.S. 111 (1942) which opens the door to abuse the Commerce clause power. SCOTUS has since doubled down on that Commerce clause power, using it to uphold marijuana prohibition (Raich), and laws against guns that were NEVER in ANY commerce, let alone interstate commerce (Stewart).
The beauty of FR is the variety of expertise available to contribute to any discussion; even legal ones.
Of the hundreds of thousands of laws still on the books, I am sure someone will find one that nullifies that Supreme Court decision. No sense bothering the Supreme Court with details...
At this point, what difference does it make?