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Why do you believe Twitter is not qualified to pass judgement about what content is and is not acceptable on their platform?
If they don't have the right to do so, then who does?
As you suggest, there is no absolute way to appraise societal interest, since interest is in the eye of the beholder.
The value of the methodological shift TFA highlights is not to define a societal interest but rather to change the way content is evaluated.
Instead of using the first amendment as a metric, TFA says social media proprietors are now using a different frame - whether content is in the society's interest or not. That's something that individuals are free to argue and differ about, which of course they will, in each individual case. The point is, to win the argument, they have to demonstrate something different than conformance with the first amendment. They have to make the case that including or excluding certain content makes the world a better or less worse place.
This change leads to debate and consideration about the merits of content, or at least, its effect on members of the polity. Using the example of holocaust denial, which gets a free pass when judged only by the first amendment, an argument about censorship has to take account the impact of the speech on individuals. That's a significant step towards enabling empathy, which might actually improve the quality of public discourse.
the problem here of course is that it is not so easy to define what "societal interest" are at any moment, plus what makes Twitter qualified to pass judgment?