The easiest way to explain why ANSI contrast is the better way to measure how good the contrast is for a projector, ANSI contrast refers to the difference between black and white when they coexist in the image. In other words very different from setting up a black image, measure, setting up a white image, measure and divide the result on white with the result on black. With ANSI, you measure black and white in the same image together.
The fact that you project white and black simultaneously on-screen means you take into account reflections and flare of the projector and the room. Light intended for the white squares will find its way and fall onto the black squares where they will raise the light level and reduce the contrast ratio. This is what happens in real content, so the test pattern should reflect the phenomenon. Inside the projector, light scatters in the optical elements and leaves the lens in places where it is not intended to be. This is impacted by the material quality of the glass elements, fringe effect, light absorbers and coatings inside the projector, but also by the inherent light modulating technology used (DMD, LCD, LCOS …). In the end, it relates more to real images as it has white and black in the image at the same time during measurement.