I don't think so.
I mean, I see what you're saying, that many of these demands on our attention are extraneous—bordering on useless. But, and I speak from personal experience as someone who struggles with executive function, that as a problem is disconnected from executive function. To me, what executive function means is that I have projects that I am interested in, that I would like to work on, that I would be happier for having completed, that I am unable to complete. That, like the subject of the article, I want to go and meet my friends for lunch, but have to cancel. Eradicating the 'productivity culture' might, as a side effect, reduce the level of executive function required, but they are not tied to one another. Having executive function means being able to do the things that I want to do, when I want to do them.