Because it doesn't add another term to the length element?
One way to understand the dimensionality of space is to examine the nature of the length element. In three dimensional space (and with a Cartesian basis) it is
$$ (\Delta s)^2 = (\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2 \;, $$
which you will note has three terms. In four-space it would be
$$ (\Delta s)^2 = (\Delta w)^2 +(\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2 \;. $$
Density doesn't add a term to the length element, instead it effects the coefficients of the sum. Something like
$$ (\Delta s)^2 = c_x(\Delta x)^2 + c_y(\Delta y)^2 + c_z(\Delta z)^2 \;, $$
with no guarantee that the $c$'s are unity.
That's a different kind of modification to the meaning of space.
Aside: This kind of definition has a couple of nice features. First, it extends smoothly to include intervals in Minkowski space or the more generalized space of general relativity. Second it allow a clear explanation of why the proposed compact dimensions of string theory don't appear to effect physics at human (or even nuclear) length scales.