Depends on the type of pixels. Dull or pretty ones?
Games are about art style and art people's ability to tweak stuff to look pretty. Procedural stuff doesn't lend itself to that, that's why it's not very viable for AAA development.
This and memory access. But w/o dedicated HW to do procedural stuff, you're trading a lot of compute power to do stuff like marble. Or any noise for that matter. Where do you get your random data from? Texture? Cool but your point was to minimize texture (or data in general) access. And then you've got to do a lot of postprocessing on the data itself which takes cycles. A lot of them.
The discussion wasn't really so much about procedurals, but I do want to address this because I still see it all over the net.
The idea that you can't use procedurals to do artsy stuff is somewhat of an old myth. That was mainly the case when developers couldn't spare the polygon budget to model small objects and procedurals were plain, simple and in their inception.
Take for example individual pieces of a character's attire. They would use textures or images, because they could draw the belt buckles, and the buttons, and add some touches to that 2D image. Or they would model them in 3D, but then unwrap the characters, turn the detail into 2D images which would later be skinned and the 3D detail brought back to life with some sort of bump mapping. The latter process is still common place today, but it has changed somewhat.
Now we are also beginning to display the 3D belt buckle in-game as a 3D object as well for the up close LOD models, the models closest to the camera. What we need now is to be able to show the leather texture pattern to make it look realistic and be able to zoom in on something like that and maintain clarity and resolution. Now you would use procedurals for that texture. Static images would lose out if you have the processing to spare. And that goes for the remaining pieces of your attire.
There's also a lot of new tools for procedurals today that allows for things not possible before. You can actually use them as a brush and mix them with image textures or other procedural to create a new regular image textures, or draw directly on a character. So a portion of your character's pant leg might be textures with one procedural, and another portion out of another, and in between you can have a static image if you so wanted.
If you're creating a 2D side scroller, and you really want hand drawn art, or a very cartoonish game, or something like Porject Spak, then you're still going to rely for good old fashion 2D images for a lot of your art, but for 3D games things have changed a lot.
Whether it's dirt, whether it's cloth, whether it's leather or metal...now that we're at a point where we're displaying the material's actual granular texture, procedurals are going to play a big role and could soon enough unseat image texture for the most commonly used types of textures in games. And all the arty stuff will still be there, but they be using actual 3D geometry to sculpt it out and present the art style. A lot of what used to be done in a 2D paint program to create a 2D image that would then be skinned on a character, is starting to move over to actual 3D sculpting using actual polygons and painted with procedurals, which now we have the power to carry it over to the game engine itself.
You can also animate them just as you do gifs but they require far less space to do so which is a big deal. Using animated procedurals with bump-mapping or displacement or even tessellation and realistic lighting can lead to some really interesting looks and effects.