The FCC has no authority to regulate cable or the Internet.
"The Federal Communications Commission (FCC) is an independent agency of the United States government that regulates communications by radio, television, wire, satellite, and cable across the United States. The FCC maintains jurisdiction over the areas of broadband access, fair competition, radio frequency use, media responsibility, public safety, and homeland security."
It's true that the FCC doesn't regulate internet content, that's why classifying sites as publishers would be useful. We would have the same legal tools that apply to newspapers.
Has their ability to regulate communication that doesn't involve any public resources ever been tested in court?
You could easily argue that things like ISPs require content-neutral regulations, but for regulating content there needs to be a pretty damn solid justification for why the First Amendment can't apply as written. For public airways the bandwidth is limited enough that allowing some speech necessarily comes at the expense of other speech, but that justification is very shaky for cable and satellite TV, and it completely falls apart for internet services. It would be comparable to the federal government trying to regulate the content of private correspondence through the postal service.
"The Federal Communications Commission (FCC) is an independent agency of the United States government that regulates communications by radio, television, wire, satellite, and cable across the United States. The FCC maintains jurisdiction over the areas of broadband access, fair competition, radio frequency use, media responsibility, public safety, and homeland security."
https://en.wikipedia.org/wiki/Federal_Communications_Commission
It's true that the FCC doesn't regulate internet content, that's why classifying sites as publishers would be useful. We would have the same legal tools that apply to newspapers.
Has their ability to regulate communication that doesn't involve any public resources ever been tested in court?
You could easily argue that things like ISPs require content-neutral regulations, but for regulating content there needs to be a pretty damn solid justification for why the First Amendment can't apply as written. For public airways the bandwidth is limited enough that allowing some speech necessarily comes at the expense of other speech, but that justification is very shaky for cable and satellite TV, and it completely falls apart for internet services. It would be comparable to the federal government trying to regulate the content of private correspondence through the postal service.