"This Constitution, and the Laws of the United States which shall be made in Pursuance thereof; and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land; and the Judges in every State shall be bound thereby, any Thing in the Constitution or Laws of any State to the Contrary notwithstanding. . . . [A]ll executive and judicial Officers, both of the United States and of the several States, shall be bound by Oath or Affirmation, to support this Constitution." If the constitution is the supreme law, and the judges must support its supremacy, the only way I can perceive of upholding this is by way of judicial review. It might not be explicit in the constitution, but this is a very strong implication.
Fuck your implication because
The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people.
It is The People's job, or perhaps the State's, to decide if abridging our freedom of speech, including yelling "Fire!" in a crowded theater, is Constitutional.
Since the 10th is being ignored, then who the fuck cares what the rest of the Constitution says? The Constitution says that no law can abridge the freedom of speech. But we now have definitions of what is "protected speech" and what is not. Some of it is covered by the Constitution, and some is not. Same with guns, and trials, and warrants, and everything else in there. The "Supreme Law of the Land" only applies when the Supreme Rulers of the Land decide it does... which means it, including the part you quoted, is as valueable as King George's pinky swear to not abuse the colonies.
Welcome to earth, citizen.