Using the contrast control lower the contrast ratio of the display.
Digital projectors have a fixed contrast range capability between black and white, let's just pretend an abstract. The blackest the display can get is say 5(because it's not completely black), and the whitest is 100. The idea of calibrating a digital is to align the source black output to 5, and the source white output to 100. If 100 is too bright for you, and you lower the white to lower than 100, you are reducing contrast ratio because black is still at 5 (as low as it can go) but white is now dimmer. By using an ND filter, you lower both the same amount so the ratio (your contrast ratio) stays the same. You might end up with a white of 50, and a black of 2.5. That way you've lowered BOTH your black level and your white level by half, maintaining the same contrast ratio as before, but now you have reduced light output.
That's why you don't use the white level control to dim a digital projector, because you lose contrast by wasting part of the available limited range that you have at your disposal.
Digital projectors have a fixed contrast range capability between black and white, let's just pretend an abstract. The blackest the display can get is say 5(because it's not completely black), and the whitest is 100. The idea of calibrating a digital is to align the source black output to 5, and the source white output to 100. If 100 is too bright for you, and you lower the white to lower than 100, you are reducing contrast ratio because black is still at 5 (as low as it can go) but white is now dimmer. By using an ND filter, you lower both the same amount so the ratio (your contrast ratio) stays the same. You might end up with a white of 50, and a black of 2.5. That way you've lowered BOTH your black level and your white level by half, maintaining the same contrast ratio as before, but now you have reduced light output.
That's why you don't use the white level control to dim a digital projector, because you lose contrast by wasting part of the available limited range that you have at your disposal.