Why Frenkel defect does not impact the density of the solid?
The sources may not explicitly say this, but I suspect that they consider mass density to be a macroscopic property, to be measured from at least milligrams and cubic millimetres.

If the volume considered is small enough, then yes, one would see local variations of the density. However, if you make the volume even smaller, you would see huge variations in the density as additional nuclei are included. (Similar statements will be true for Frenkel defect concentrations.) On this level, the definition of mass density simply breaks down and is no longer very useful.