However, the situation you outlined still occurs because you can get stuck in a certain paradigm (e.g. "this name that I can't remember definitely starts with 's'"), which you effectively reset, in addition to simply returning re-energised. Still a good argument for breaks and less strenuous working hours.
Every now and then when I'm doing English to German translation, I find myself puzzled and then have to remind myself "think about the Dutch word" only to then immediately understand/recall the German cognate. I'm sure someone talking to me in Dutch could have the same effect, and more broadly speaking, another 'attractor basin' may be activated by random chance, like the tired cliche of someone in a movie figuring out the 'case' as a result of their spouse or child mentioning something unrelated yet apparently analogous.
Though I feel that System1 can't work while System2 is focusing on other stuff like playing games or browsing social media so I don't think they're necessarily running in parallel.
Many of my more annoying problems have been solved that way.
I knew an old Vietnamese refugee who was an electrical engineer working on maintaining and repairing portable stage lighting ballasts. He used to tell me how he would dream about the circuits and debug them then after spending a week of just staring dumbly at the physical thing—not accomplishing anything while at work, then come in the next day and finish inside of an hour.
Maybe I think much differently than others, but sometimes on difficult problems I will think forever and do nothing. In the interim, people will think I'm an idiot ("don't you have work to do", "shouldn't you know this"). Then suddenly, whoosh, everything comes at once. I'll work for a comparatively short amount of time, code/work will just fly from my fingers, and whatever I'm working on will be excellent quality. One of my finest moments was in the process of one of these outbursts I was able to write a "one shot wonder" class that worked essentially exactly as expected without rewrites (no compilation errors or defects).
This is just kind of how I operate, and it really held me back in college (decent exam scores would bail out awful homework scores) though now it's nicer in a professional/adult environment where people give you a little more leeway, freedom, and respect. Though the drawback is that it ruins metrics like burndown charts and managements' expectation of a proportional work-to-output ratio.
If I do have a huge deadline and have to double or triple that in a day I find myself mentally wiped and kind of useless for several days there after.
But those nagging administrative tasks, status reports, talking to project management professionals in pro-forma meetings. THOSE are considered work and productivity for the people that set these up. There are job-roles for which meetings themselves are work-- while that might be a vision of hell for many of us, it is reality for layers of management and their minions.
My concern with this concept of 4-day workweeks is that it will precipitate even more tracking of productivity and even more meetings to gauge progress at the organizations that are trying to convince themselves to switch.
There's something to be said for having the slack to figure stuff out at work without being tracked constantly. A shorter work week is likely to increase "time scrutiny" for creative workers.
In answer to your question, DHH of Ruby on Rails fame used to write a lot about 37 Signals and Basecamp. They decided that the normal capitalist way of working was a load of rubbish and that they could get more out of people by making them work a lot less hours.
The way our world works is a system, the capitalist system, and with it there are many things that go unquestioned. Employment is seen as good whereas in a parallel future that never happened there was this idea that we would all be working a mere handful of hours with the machines doing all the heavy lifting. We live in an era of bullshit jobs to maintain the system with something like 87% of people actually hating their job. In the conventional sense Hemingway did not have a job. As a programmer with many interesting problems to solve creatively there is no need to be part of the 87% and to be more like a Hemingway. The DHH's of this world do not hire the 87%.