It's a podcast — audio and transcript at the link — with various Atlantic staff people (Kevin Townsend, Sophie Gilbert, David Sims, and Spencer Kornhaber). I have seen the movie, by the way.
I think the quote I put in the post title is trite and foolish. The difference between the present and the past is the present is where you're living now. It's self-involved to believe that in the past, you could do parody and satire, but now — now! — things are already so absurd that there's nothing to add, no way to exaggerate, and we're suffering in some extreme new way that makes comedy impossible.
But let's see what these people have to say:
Sims: You could make a more straight-ahead blockbuster movie.... But... this flirts with being... more like a Dr. Strangelove kind of movie. A pure anarchic satire that is set in the real world, but every character is cartoonish, and there’s no sense of humanity whatsoever. But Don’t Look Up tries to retain this core of humanity...
Gilbert: [T]here was the idea that Trump defied satire, because he was bigger than it could ever manage to be in its wildest imagination. I also think it’s really hard to satirize things when you’re in the middle of them.....
Kornhaber: I think this quest for movies to deliver a message that changes people’s minds is maybe quixotic. There aren’t a ton of works in history like that.... True, you can’t really satirize Trump. He’s kind of beyond parody. But you can call attention to the dynamics of the way that people relate to him and the effect he has on the world around him—and on the viewers themselves.
Comedy is hard! It's not enough to sign up a lot of stars and spend a ton of money and pick an important topic. Why would you expect it to be good in the first place? Dr. Strangelove is great, but you have to make some choices and exercise discipline. Sims reveals, based on an interview with the director....
DiCaprio was obviously interested in the project and the message but was not going to commit until they’d figured out his character. He clearly did not want to be in a cartoony pastiche movie.
That precluded the Strangelove approach. I'd like to see a comedy about making "Dr. Strangelove" in which all the actors are divas insisting on their character's humanity.