While rendering without vertexes is very possible, it is FAR from efficient.
The thing here is, that it boils down to writing very complicated and convoluted fragment shaders. This approach, while cool in theory, has massive drawbacks.
- It is hard to debug
- It is very inefficient as far as processing time goes.
Basically, you need to run a very complex algorithm for every single fragment on your screen to determine its color. As you can imagine, this means repeating your calculations hundreds of thousands of times, even for a 720p render. For each frame.
Furthermore, while I never studied this in-depth, I believe there are limitations to what exactly you can do with it. Many GPU's, especially on mobile, have a limit to how many instructions long they can be. And if you want to create something like an animated character, you have to basically emulate vertexes to at least some extent within your fragment shader, so you can keep track where his limbs are and his position on the screen. So you return to vertexes, only in the least efficient way.
That's what I think about it. I may be very wrong here. But I personally think that it's a cool exercise and nothing more. Essentially, it's a waste of time that has only bragging rights for benefits.
There is a reason why all modern rendering is vertex-based and texture-based and polygon-based. Because it greatly reduces the processing needed, and as such lets you do more MEANINGFUL calculations.