Well you have just asked the $64,000 question and I will weigh in with my thoughts knowing they somewhat go against conventional wisdom. At least some peoples conventional wisdoms.
Keep in mind these are my opinions and most haven't been proven thru testing.
First off a lot of commercial screens have texture. The texture they have is very fine and is defiantly in the many times sub pixel range but not microscopic. Any flat paint has texture but the texture is on a microscopic level. So I would think of a painted textured surface as having a texture over a texture. Like grass growing on rolling hills. Both textures have the ability to make the light scatter in all directions when striking the screen. Assuming you want a screen surface with diffusive qualities you will want one or both of these types of textures.
Secondly the opposite of texture is sheen. Sheen or gloss causes light to reflect in less of a random manner and more in the manner a mirror would. The angle the light strikes the screen at is about the angle it will leave at. Thus directional gain or gain in brightness at the expense of viewing cone.
IMO most of the DIY screens of late mine included have a combination of both modes of light reflection. Its common to use poly ether on top of flat paints or mixed with them to add a component of sheen to the surface or take away some of the texture if you want to think of it that way.
One thing I know for sure about painting over a textured surface is the texture has to be sub pixel by about a factor of 10 and the texture has to be uniform across the whole screen surface. Any change in the texture will show up in motion shots. It will be like something is moving across the screen but the slight change in the image because of variance in the texture will be going the other way. The object of a screen IMO is to not know it's there. It should look like looking thru an open window.
My screen is painted over a fine weave canvas and the texture of the thread count helps in a couple ways I feel. First it softens the lines between the pixel blocks. Secondly the texture helps the person not as skilled in painting produce a uniform surface. And lastly the texture allows one to paint with a slightly higher sheen paint than they would over a glass smooth surface. I think the micro and macro textures can work together.
I do know I couldn't have used the same paint mix I used and brush painted a smooth hard surface and not had tons of brush marks and inconsistencies that would have caused PQ issues. The smoother you go for sure the higher the skill level.
Below is a thumbnails of a close up of my surface. Its not pretty viewing at 2 inches but at 12 feet I'm more than happy. Click to see larger.