> The first amendment has the egregious exception for obscenity with an absurdly subjective community standards test.
True, that is a problem. I'd say it's smaller problem than "hate speech" ban though - it's quite hard to ban something important to the society under obscenity ban - after all, not a lot in our life depends on being able to see tits (or whatever bits one is personally fascinated with). But it's quite easy to disrupt democratic processes under the guise of fighting "hate speech" - see Russia, for example, with its infamous article 282. I'm not saying US censorship is good - on the contrary, it's despicable. But it's a) less dangerous than European one which has clear political goals of suppressing political opinion and b) clearly goes contrary to a supreme law of the land that states freedom of speech shall not be infringed.
> The first amendment is only applicable to the government as an actor.
Well, yes. But only government is an actor that is allowed to use force, so if the government is banned from interfering with your speech, that's a big deal. Of course, private citizens can refuse to talk to you or interact with you because of your speech and that'd suck. But at least they can't force you to stop speaking or jail or harm you for that - or, at least, if they try, the state will be on your side.
> Americans are all too willing to refuse to label censorship by parties that are not the government as censorship
No, labeling is fine - it's just that private censorship is different, as per above. Publishing stuff in other place than Facebook is much easier than moving to another country.
> Book burning is still book burning.
Yes, but if I have bought a book I have the right to burn it. It's my book, I do what I want with it. And anyway, how me burning my own book hurts you? You can buy your own book and not burn it, I don't prevent you from doing it.
> the whole reason for that censorship is this one defect in the first amendment
Nope. You seem to be misunderstanding what US Constitution is made for. It's a unique document, and often misunderstood. It describes what Federal Government can and (very important) can't do. But it doesn't - and can't - describe what private citizens can and can't do, because it's citizens establishing the Government, not the other way around. So it's not a defect, it is by design that Constitution can not limit private citizen's actions.
> The irony being that the exception isn't even in the first amendment,
Again, private censorship has nothing to do with First Amendment. The infamous "obscenity exception" and other "exceptions" of the First Amendment invented by various political actors always have one goal - to enable the government to restrict speech. Nobody uses them to make The New Yorker magazine to publish porn - only to ban some other magazine from doing so. First Amendment can't make The New Yorker publish materials they don't want to, but it can protect Penthouse from being shut down by the government for publishing something they do want to.