Perhaps we have a different interpretation of the screendoor effect?
The screen-door effect (SDE) or fixed-pattern noise (FPN) is a visual artifact of displays, where the fine lines separating pixels (or subpixels) become visible in the displayed image.
It doesn't depend on resolution, it's the structure of the display becoming visible. With soft focus and pixels that don't leave big gaps between them, you will get a softer picture, yet less intrusion from a fixed grid always being visible.
There were better screens around at the time of the NES. PC was switching over to EGA and already had much higher resolutions. Yet the games were better on the NES. So will the games be better on the Switch than on high end phones. Even though the install base for phones is much much higher, (and incomparable to PCs at the time of the NES) they're still not getting any $60 game experiences. VR will remain a gimmick on phones until people start willing to pay for games on phones.
I m sorry but ur interperatation is not correct at all, its basic math and any display or tech enthusiast will tell you that without reaching for an article. DPI is based on resolution, lower the resolution on a large display bigger the pixel will be, it is irrelevant in which order or shape they are laid out.. if a display is big, the pixels be it square or circle in RGB patter or Diamond with sub pixel, extra pixels, they will all be large and will be visible when magnified through VR optics, hence lending to jarring screen door effect.
And for your last statement you just proved my point, VR on phone is a gimick and nintendo is adopting it and further downgrading it, hence no matter how great the game is if a player doesnt enjoy on the hardware it is being played, then there are always better alternative to do so on phone with much better screens and gyro.
DPI has little to do with screendoor effect.
My first experience with projectors was a CRT projector, 500 scan lines or so. You have to manually adjust each lamp so the scan lines overlap eachother. Focus too perfectly and you leave black horizontal lines in between, as if you're looking through sort of a screendoor. (Except only horizontal lines as CRT scans continuously from left to right). More lines, smaller gaps ofcourse, or adjust the focus so the lines are bigger on the screen so they touch, removing any black in between.
It's the same with LCD projectors (and DLP although I have less experience with those). If set perfectly sharp, you will easily see the pixel structure. The trick is to project the pixels slightly bigger so they touch. That's ofcourse easier and yields better results when there are already smaller gaps between the pixels and more importantly with pixels of even size and distribution. Pentile is the worst for screendoor effect.
Screendoor is more noticeable in VR, since it shows up as a fixed screen that turns with you as you move your head. The world in front and behind it stays in place and the movement between the two makes it stand out. Sure make the resolution high enough and the screendoor will be so fine you won't see it anymore. We're a long way of for that. You need at least 100 pixels per degree for that, or 10k per eye for a 100 degree fov headset. There are ways to mitigate the problem, which are a lot easier to do with a fixed headset instead of a universal one, and with RGB displays instead of pentile.
As for Nintendo further downgrading it, sure I would love psvr to be a massive hit and sell tens of millions. Just not gonna happen anytime soon. Neither is OR or Vive, and while there are many headsets out there for phones, there are no custom made full VR games being made for them afaik. Nintendo Switch has a chance to have both the audience and the software, although not the tech.
I was wowed with Descent 2 in stereoscopic 3D at 320x240 at 60hz on a 72" screen with that CRT projector. Flicker glasses so only 30fps in the end. It worked fine, looked amazing. It didn't last though as stereoscopic 3D by itself doesn't do much for games. It's all about headtracking, being in the world. I'm more worried about Nintendo Switch's inability to do positional headtracking than the screen resolution. Hopefully it will do something for that as it transforms the experience. I wasn't impressed at all with 360 videos until I saw this last night http://www.tomshardware.com/news/joshua-bell-vr-experience-launches,33662.html Positional tracking makes all the difference. It doesn't have to be much, just enough to decouple the screen from your head movements.