The founding fathers never watched CNN.

Just an antecdote, my liberal uncle regularly post stuff claiming fox and other conservative outlets are "propaganda" and should be banned, and praises other countries that have supposedly already banned them (I haven't looked up the accuracy of the claim) as "propaganda".
I agree that defining "offensive" speech in order to claim it isn't protected is a direct threat to free speech.
("Propaganda", "hate speech", "anti-science" ect.)
Of course we already have certain limits such as "yelling fire in a movie theatre" (likely to cause an immediate dangerous panic) or making threats of physical violence, so some speech is limited, but based on a more imediate and substantial threat.

No media outlet "should" be banned but they want to control us through lies, manipulation and omission. There was a time where "Journalistic Integrity" was voluntarily followed but the National Enquirer showed all the other media how to be bad and get away with it. If the corrupt media wants to "self police" I'm sorry but I trust them less than the government.

Since it doesn't define "the press", it pretty much is useless.

Speech and press are listed separately in the first amendment. "The press" clearly referred to the printing press. But was clearly included to address that freedom of speech extends beyond the spoken word.

So the problem remains. "Freedom of the press" means whatever you want it to mean. If the term "press" is left undefined then anything and everything is a "press" and the government cannot do anything.

That is not a problem. What it means is that the government cannot ban any speech. That is actually the whole point of the amendment.

And we now know they can just "Alex Jones" you. Shut down free speech by attacking the medium you use via a 3rd party that isn't bound by the constitution.

Unworthy or not it's still considered freedom of speech, and you have the choice whether to believe it or not.
Take where I live for example, there is one local paper that the city basically gives it's yearly operating funds to, So it will be the propaganda piece for the city's spin.
Although personally I kind of think it's fun to unravel the spin and find things that they want to keep hidden. Hidden horrors is what I called them in my last city council presentation. Like my most recent finding involves nepotism in awarding of city contracts. And unless someone is willing to say it to the public, the public doesn't know.
Again being put at a disadvantage...
Only upvotes! :)