1) The US Government does not own everything these systems run on. Companies own their own property.
True ownership means control. You don't control it if the government can shut you down (eg. through heavy fines) for highly subjective activity.
there are some well-known limitations (like shouting "Fire!" in the theatre when there is no fire).
That one always comes up. Recognize that that's another case of private control of speech, and the theater is justified in controlling what's said there.
The problem arises when the government can tell a private company what information (ie. imagery, photons, bits) is not permitted to be disseminated, because it offends some segment of the populace with primitive mores that the company might employ.
You, of course, have the right to not fly American Airlines if you don't like this policy and fly Hooter's Air instead.
I do wonder how Hooters manages to evade these laws. Probably just a matter of time, though.