You're confusing a diffuser with a true, anti-glare coating. Indeed, a "diffuser" does what your suggest, and the aftermarket applied films for glossy displays accomplish this function.
However, a proper anti-glare coating doesn't function this way at all. It involves the very careful deposition of a thin film of precisely controlled thickness and index of refraction, often multiple layers, to take advantage of the destructive interference of the wavefronts of the reflected light from the various film/film and film/glass interfaces. This literally cancels the glare or reflection.