Nearly every right is limited in some way "for the good of society". You can't take pictures of the entire contents of a book and publish it. You can't run into an airport and yell that you've got a bomb. We, as a society, put limits on what we allow people to do because doing so is better for society as a whole.
I expect there are plenty of cases where you can't publish your video feed.
> You can't take pictures of the entire contents of a book and publish it.
Copyright is "mostly" civil law, not criminal.
> can't run into an airport and yell that you've got a bomb.
Right: now try and argue that a license plate intentionally designed for public visibility is somehow subject to the same restrictions. All 50 states have legislation requiring public display of these objects: what tailoring of the First Amendment would legally be consistent with past case law?
> I expect there are plenty of cases where you can't publish your video feed.
Legally these cases are few and far between, and none of these exceptions apply to the situation being discussed. You're welcome to try and cite a case or explain relevant case law - good luck.
Freedom of the press is extraordinarily broad and is one of the more difficult things to limit using criminal penalties.
You are of course correct. There are always limits on speech. In this area, however, we have already decided how it works. You cannot regulate what private citizens record in public spaces with no expectation of privacy and you definitely cannot regulate what they do with that data.