I think this depends a lot on whom you think things aren't being made clear to. Given who the NYT audience is (72% have a university degree, 91% identify as Democrats), I think most of the readership is going to be in the pro-science mindset.
More that that, regular readers of anything learn to interpret in context. E.g., I've long read The Economist. People reading one article there might see them as dull. But as a regular reader, I know they can be brutal; you just have know which particular dry turns of phrase indicate the brutality. I think most NYT subscribers will know how to parse NYT articles and pick up the condescension and undermining in the article.
I'm not saying you're wrong, but I don't really see it as a complete defense. I would expect the point of a paper of record to be that you can take its reporting at face value. If you have to be familiar with its cultural conventions to understand what the reporters are really trying to say, doesn't that still boil down to, I'd better be careful when reading the paper or I might end up misinformed?
If nothing else this should be clear already from these past years. Very few journalist has the kind of absolutely maniacal approach to understanding the world, placing a particular story in it and then effectively communicating it that would be required for blindly trusting a paper of record.
I don't think that the typical view of Gell-Mann amnesia is correct. I think there are issues, topics that are pretty much reliably communicated. Probably local issues, politics, and maybe that's it. Everything else that requires deeper context just gets at least one thing wrong. How wrong is of course an important question, and is usually paper and journalist dependent. (But for example anything involving economics, psychology, AI, the sciences... are suspect.)
I think you're packing a lot into "face value". Off the top of my head, I can't think of a source that I don't understand better once I've read a bunch of it. Words get meaning through context, through expected shared understanding.
Exercises in "true" simplicity end up having their own problems. For example, Up Goer Five [1] and Thing Explainer [2]. Or less cartoonishly, Simple English Wikipedia [3]. There are reasons that more advanced topic are covered in more advanced ways.
More that that, regular readers of anything learn to interpret in context. E.g., I've long read The Economist. People reading one article there might see them as dull. But as a regular reader, I know they can be brutal; you just have know which particular dry turns of phrase indicate the brutality. I think most NYT subscribers will know how to parse NYT articles and pick up the condescension and undermining in the article.