What's the practical use for understanding that intuitively (for the 1000s of people who have to go through it every year)? Genuinely curious.
This is the first, simplest, off-hand example I can come up with.
Things are blocked "in parallel" (assuming the camera is far away from the objects) because that projection is a linear map (I repeat, assuming "far away focus") and has a one dimensional kernel: 2d + 1d = 3d, which means (flat TV + orthogonal lines = 3d world), that is the dimension formula.