Buddy. Please. Commerce clause is the grant of power that allows such regulation to be promulgated by the Fed but it must still pass First Amendment muster because it is a regulation of speech. The enabling articles grant power while the bill of rights limit power. Saying that the commerce clause (enabling) permits X, and therefore X is unrelated to the First Amendment (a limiting clause) is nonsensical.
Numerous regulations on commercial speech have been struck as violative of the First Amendment. Some have survived. It's regulation of speech.