You are saying that the image assumes a physical size on a monitor, which is not true. It is only in output to physical media (not a screen) that the image assumes a particular size.
Why do you think that a monitor is not a physical media?
Can you measure it? Of course.
Can you measure the image size? Of course.
It is the pixel dimensions alone that determine their size on this medium.
As I said pixel is adimensional until you render it as one or many dots.
The reason PPI isn't taken into account for screen display is that on a monitor, the PPI is fixed - and every monitor is different. A 26" monitor with a resolution of 1920x1200 will display everything at 73.84PPI (1920/26). A 24" monitor with the same resolution will be 80PPI. You can't cram the monitor pixels closer together, or push them further apart.
24" or 26" are the measure of the diagonal.
But it's true that the dots (DPI) are rendered at a fix PPI value (DPI=PPI).
If the screen resolution is 1920, then you can display a 1920 width image.
But the rendering application fix the image size, and it can go up or down from 1920 (resampling), before passing the image to the graphic card.
A printer can work at different output resolutions (DPI) (not many, generally 2).
As you set the printer quality, the driver sets the corresponding DPI and PPI value.
So, after setting the printer preferences, there is no difference between printer and monitor.The DPI value is fixed, the PPI value is fixed.
The ultimate rendering application for printer is the driver. The driver satisfies the request for a print size, so resampling is performed if the PPI value is different from the expected one.
On paper, the effective resolution is much higher because we don't have a predefined pixel size.
The DPI value can be equal to the PPI value. This is true for contone printers.
For inkjet printers,there is a difference. Ink colors are limited, so a dithering is applied to try to get a visual appearence similar to the original color. This explains why the DPI value is bigger than the PPI value.
After re-reading Jacopo's posts, I think part of the problem here might be a language barrier - and we may both be saying the same thing. If so - my apologies