Does the value added by sources like the NYT outweigh the negatives of being occasionally biased or outright wrong? Yes.
The only "values" that matter are the personal whims of whoever happens to own Twitter, or Google or Facebook.
NYT may have more reach and definitely isn't neutral, but it's a far cry from the nonsense that Breitbart publishes. It's nakedly partisan.
What gets a website censored, in the modern corporation-dominated Internet, is going against the interests and preferences of Big Tech owners - and nothing else. Nobody with any power is bound to look out for the public interest, however defined; ICANN is perhaps the only exception that comes to mind.
We can waste our time and attention debating over which targets were more or less deserving of censorship, based on our personal ideas of public interest. But as long as Big Tech is allowed to exist in its current form, we're like powerless peasants arguing about the decisions of kings.