High relative density (RD) is the criterion and not high density to obtain appreciable mechancial properties of composites.
If you contemplate the relation between the percentage porosity and fracture, you will understand the significance of getting the RD of above 99% in composites.
High density usually implies a low void density, which normally act as stress risers at the corners and edges of the internal voids and therefore becomes potential sites for the crack nucleation and propagation upon the application of external loading whether it is static(fracture) or dynamic (fatigue) in nature. Situation would be extremely critical if the matrix itself made out from the brittle material to be used at low temperature environment and in saline waters (operations in arctic waters).
The mechanical properties of a fibrous composite are determined by the volume content of fibers (load-bearing elements of the material structure) and the strength of the interfaces between them. The relative density of the material, its color, taste, etc. are secondary factors affecting the mechanical properties in the second, third, etc. queue.