Why does Minecraft use polygons to draw the world terrain instead of voxels? Would a voxel based rendering engine be appropriate for a fully destructible game world built out of cubes like Minecraft? Would it be more efficient than using polygons?
Graphics hardware works with and renders triangles, so you have to use triangles if you want hardware acceleration. Most voxel renderers employ something like Marching Cubes to extract a polygonal mesh from a voxel representation and present that; direct volume rendering is typically computational expensive.
Probably, but not because voxels are faster or cheaper to render (in fact, they're more expensive to render since you must convert the data set). Voxel representation lends itself to manipulation easier than polygons -- so it's much easier to add and remove chunks, bits and pieces of the world represented by the data set.