Satellite and cable broadcasts are not broadcast over the public airwaves. They are broadcast on privately owned satellite and cable systems.
This is a simplistic and largely inaccurate view.
A recent study found that while only 6% of Americans identified as far-right, just 8% saw themselves as “progressive activist”/far left. So you could as easily say that most Americans (the “exhausted majority”, 67% in this study) “detest” a sizable proportion of this message board. 
The U.S. voting population has long been considered “center-right”, though that doesn’t mean Republicans hold sway (they arguably would win more elections if they could keep from being dominated by their more committed rightist elements).
The Left would benefit if it was less obsessed with the Evils of Fox (which is more of a symptom than the disease) and ceased dreaming of a renewed Fairness Doctrine, which never worked all that well and is outmoded now due to the multiplicity of news outlets which don’t depend on the public airwaves, so that anyone can readily find a biased source that they like.
Many (most?) people, despite their claims, don’t really want an even-handed, “fair” news media. They want to hear their views reinforced.
Despite the defects of “capitalist” news media, it’s infinitely preferable to state-run news media.
FCC regulates all telecoms with regards to the *technical operational *aspects. Don’t interfere with other signals, leave this channel open to responders, don’t have a beam so powerful you cook birds flying by at 100 yards. *Content *OTOH is only regulated on the open-air broadcasters. And the legal precedents supports it being that way.
Before there were radio and TV, newspapers were (and continue to be) absolutely free to have a completely partisan editorial line. Of course, they then were responsible for what they printed, if someone had the resources to sue. Which is why there has been a question for decades if first ISPs and later online venues are carriers, aggregators, or publishers, since that can affect to what extent you are to be responsible for the content – I’ll readily admit many online outfits want to have it both ways.
Neutral statements of fact do not sell ads. They figured that out way back.
We are seeing a bit of a rise in “fairness” concerns from the right when it comes to private capitalist venues like Facebook/Twitter etc. deciding whether or not to fact-check and YouTube demonetizing channels that YouTube deems controversial (or that get too many complaints for YouTube’s patience). So yeah, the whole construct seems entirely subject to who’s goring whose ox.
What you say iis true, but would not be defensible, under the basic principle of regulation, which is defensible’