What operations are we interested in?
We need to decide, what operations we want our model to have. In other words, what is the definition of a query?
It is desirable that our operations on multidimensional objects return multidimensional objects as well, so that we could issue queries against them again.
We can always consider grids as unions of cells and say that any operation that maps a set of cells into another set of cells is acceptable (this would closely follow the fact table representation of cubes).
But do we really want that? We have developed a multidimensional view of the world because it served our purposes well, so we would like to preserve it as much as possible.