From the book review:

Does the First Amendment's right "peaceably to assemble," for example, include the right to block traffic in the street? All liberty, whether enumerated or not, may be "reasonably regulated" to protect the equal rights of others. Does the requirement of getting a parade permit constitute a reasonable regulation of the right of assembly?
Is this really all that difficult a question to answer? I suppose it would depend on what one's definition of "peaceably" is, but I can't imagine a definition of this word that includes blocking traffic or gathering on private property against the owners wishes.

So yes, the law does have the ability to place limits on the First Amendment's right "peaceably to assemble". It is where that right starts infringing on the rights of those around the assemblers.
But Mr. Amar goes on to advocate an exception that is big enough to drive a living constitution through. "An erroneous precedent that improperly deviates from the written Constitution may in some circumstances stand," he tells us, "if the precedent is later championed not merely by the court, but also by the people." "When the citizenry has widely and enthusiastically embraced an erroneous precedent," the courts may "view this precedent as sufficiently ratified by the American people so as to insulate it from judicial overruling." When this happens, according to Mr. Amar, the erroneous precedent becomes part of America's unwritten Constitution.
I wonder what Mr. Amar believes if the purpose of Article V of the Constitution.

If it isn't to allow the people to grant the federal government new powers the people believe it ought to have, what is it for?

"Higher taxes never reduce the deficit. Governments spend whatever they take in and then whatever they can get away with." -- Milton Friedman