But how exactly would you define the "mistake made so long ago"?
Is it the free circulation of newspapers?
Would you prefer to ban journalism or restrict the exchange of information, and what would that imply for the internet?
If you ask me, it seems like the incentive "money" might be a problem.
Maybe commercial journalism and social media are the main issue?
Which is closely related to the concept of media as entertainment.
Not a new idea either, and a boring reply without a real answer, I know.
Allowing only state-sponsored journalism would not be any better, right?
Public broadcasting (as independent from the government as possible) is nice, but doesn't solve the issues discussed here.
It seems like a reasonable and common view that being dependent on other's money hurts freedom of thought and expression, which is a basic requirement for free press.
So commercial media always was the default, but being dependent on commercial success and the favor of the public always hurt the mission we ascribe to a free press.
Same goes for the requirement to entertain the readership – it cannot be disregarded, no matter how sophisticated the media we consume might be, it needs to capture our attention in some way. This differntiates writing from data.
So my long answer kind of confirms your observation that "we can't even conceptualize correcting it now". I'm not sure if it's impossible though.
I'd be curious what your own ideas are about how to "fix the mistake".
It seems like a political question for sure though.