This is entirely a theoretical question because I understand the time it would take to do such a thing would be ridiculous
I've been working with "voxels" a lot lately and the only way I can display them to a user is to either triangulate the visible surfaces or make a CPU ray-tracer but both come with their own problems.
Simply put, if we dismiss the storage space needed for voxel meshs and targeted a very specific GPU would someone who was wanting to create a graphics API like OpenGL but with "true" voxel primitives that don't need to be converted be able to make such thing or are GPUs designed specifically for triangles with no way to introduce a new base primitive?