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.
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.