Interstate Commerce could be used to thwart this, but wouldn't First Amendment be a more compelling justification?
Think I'm joking? This is the stated judicial philosophy of the majority of Supreme Court justices. There is no traditional deeply rooted in American tradition that says anything about the Internet, either.
Moreover, when taking that mode of interpretation, it doesn't say anything about the States, nor does the 14th Amendment say anything about some of the rights protected against federal intrusion by the Bill of Rights.
The Court will rely on this precedent where convenient, I suspect.