It is the "Supreme Law of the Land," treaties couldn't exist without US Constitution since it describes the process by which all treaties are ratified.
The reason the federal government has seen to encroach on the powers of the States and the rights of its citizens goes back to when FDR was President. By 1936 the Supreme Court had ruled 11 of the 15 New Deal programs FDR wanted as unconstitutional. Between 1937 and 1943 FDR had all nine of the Supreme Court justices replaced (whether they wanted to be or not). As a result decisions by the Supreme Court between 1937 and 1946 (when Truman made his first Supreme Court appointment) were entirely FDR's justices and ruled on his behalf, regardless of what the US Constitution actually said.
Which is how we ended up with the unconstitutional Social Security, United States v. Miller, 307 U.S. 174 (1939), and Wickard v. Filburn, 317 U.S. 111 (1942) among many others. It would take 53 years before the Supreme Court finally overturned their bad
Wickard ruling in United States v. Alfonso D. Lopez, Jr., 514 U.S. 549 (1995). Considering it took the Supreme Court 152 years before they finally incorporated the Eighth Amendment and made it applicable to the States, I would not expect the Supreme Court to right the wrongs done in that one decade by FDR's court for at least another century or more.
Federal involvement in school lunches began under Truman, another socialist fascist, in 1946 with Public Law 79-396. Congress had no authority, naturally, but since when has that ever stopped a fascist leftist? Truman had no authority to nationalize the steel industry either, but he tried anyway.
The people are still paying for the crimes committed under both FDR's and Truman's administration.
Source:
Richard B. Russel National School Lunch Act