But there could be some optimizations, when all 4 points are less or greater than Z buffer and some hierarchical zbuffer testing is used.

Well, GPU should get smarter. Recently it figured out how to tessellate primitives. There is a evolution here ;)

I'm not talking about 1 tetrahedron. I'm talking about a mesh made of thousands of...

For example the point light can be done like this: we take a polygonal sphere and fill it with tetrahedrons - all sharing the vertex in the center of the sphere. Other 3 vertices of tetrahedrons...

No, I'm not talking about rendering to 3D texture.
My idea is more similar to rendering lights in deferred shading.
When the scene is drawn we have a depth buffer to work with.
So for each pixel...

I don't think that it requires a lot of work as it is a convex shape. It's just a rasterization of back and front sides at the same time and getting depths.

Yes, the depth test for volumetric object can be INSIDE, not only LESS or GREATER. Or even OUTSIDE, if it is needed.

You can create any shape with tetrahedrons by putting them together just like...

Hello!
We have functionality to draw points (1 vertex), lines (2 vertices), triangles (3 vertices).
Why don't we have a possibility to draw tetrahedron (4 vertices)?

4 vertices can be projected...