Interesting idea, but how do you deal with looking at it from different angles, or close up?

This is very old idea of 3D rendering. It uses 3D texture, not a stack of 2D textures, and make slices in the plane, parallel to the screen. More advanced variation is raytracing inside the 3D texture - on modern GPUs it could be even faster than slices. It's main disadvantage compared to sprites is limited resolution (3D texture takes HUGE amount of memory). Sprites solves this because each individual sprite, representing one voxel, have its own texture (which could be 3D texture itself) - this increasing variety.