That's a dubious statement. Filling the binocular field of view is fine; it's about 120° horizontally, give or take. But past that it starts to be a problem. Generally, if you look at the screen and any edge is blocked by your nose without turning your head, it's likely too large to work comfortably on. (but still fine for immersive content like games or movies)
Of course you need two of those screens to fill your field of view, unless you have a square screen that goes below your desk, but I'm sure that's available somewhere.
My subjective impression is that the nonperipheral visual field isn’t square. I would find 3:2 displays optimal, or maybe rather 16:11. While a 16:9 or 16:10 display could be extended vertically to fill more of the visual field, that extended portion is not large enough to usefully fit a second monitor there (without head movement).
If you're like most people and the horizontal field is close to max, you'll do better stacking monitors than putting them side/side. Inter pupillary distance is a bit over 2in (~65mm), but that's usually small compared to screen distance, which is why I say roughly square (~16:14).
I tried to work on three 16:9 displays for some time, and found it exhausting. The cognitive overload isn't worth it, workspace switching with a hotkey turned out to be far easier for me. That's not even mentioning constant neck movement.
Maybe it's just me though, I can't speak for different people; but I strongly suspect it's the same for many.
I mean this doesn't seem to be true for anyone working in the trades. "Mise-en-place" allowed me to tend a 24-foot-long bar by myself with 60+ customers. At the time, I was essentially a highly trained, top performing athlete. Just because I can't see the cash register / margarita machine / well drinks / etc... it doesn't mean it's not an extension of my body.
It is possible for your entire workshop to become a second-nature extension of self, not just the desk in front of your face.
I think part of this discussion is: "What can be part of a singular focused task vs. what requires some amount of 'context switching'?" And its not always super obvious. Practicing a workflow can integrate context-switches so that it becomes one singular focused task.
But VR/AR can also assist with neurological training by allowing you to switch environments when you switch contexts. For someone who is WFH in a studio apartment it can separate their "gaming desk" from their "work desk" from their "hobby desk" ... or even their "React desk" from their "Concurrency-wrangling desk" from their "Email/Communications battlestation". This could enable much faster context switching -- meeting in 30 seconds? pop over to your "Virtual Conferencing Room". Then come back to your sanctum of concurrency troubleshooting.
The way you expressed it actually reminds me of Iain McGilchrist's "left brain" versus "right brain" thinking model, wherein the narrow-ish "task-focused" approach is typical left-brain concern (essentialist, to a fault), whereas the wider "contextual" approach is typical right-brain associative concerns ("everything is complex/connected"). I'd never noticed this ergonomics question (should I say dichotomy) could be neurologically framed that way, thanks for the insight.
I have three monitors, and it's still not enough. I would be thrilled if each of my monitors had four times the apparent area in a 3D space that layered applications and documents behind each other in some approximately intuitive way.