- assigning random Material IDs to all faces and then using the randomization by Material ID
I know of no vanilla way to do this but manually <- And that's the evil word :] Or using a script. Additionally you would fail when having a multisub material applied to the object.
- exploding all faces into separate mesh elements
Not seriously. Usually you work with parameterized geometry and you would need to destroy the whole stack. Additionally, everything else like normals / smoothing / unwraps etc. may break when doing so. Imagine a box you create with segments set to something higher than 1 as an example. Try to randomize the polygons ("faces").
If it would be technically possible to treat polys ("faces") similar to "Mesh Element"s in Corona MultiMap - that would be absolutely amazing but I fear it is not as easy.
Good Luck