It is true that the code does not care about the actual chemical identities of the atoms - they are just labels with no properties attached. The labels have an impact of the symmetry and that is fully taken into account.
It is assumed that, once the sqs is generated, you would relax it using an atomistic modeling code that does take into account elemental properties (such as "radius").
For some codes (typically all ab initio code), you have to make sure that the interatomic distance are at least physically reasonable to avoid numerical problems.
Even if you force the sqs to have a cubic cell, the non-cubic symmetry of the atom configuration will give you a noncubic elastic tensor.
The real solution to this is to symmetrize the resulting low-symmetry tensor. See https://dx.doi.org/10.1103/PhysRevB.72.144109. This is a perfectly valid theoretically justified way to proceed.
The error "Impossible to match point correlations due to incompatible supercell size." means that the composition x and cell size n you require does not satisfy: n*x=integer. This has been answered on this forum multiple times already.