Why do you suppose the structural polysaccharide cellulose does not contain branches?

This is because cellulose is composed of beta glucose units, unlike starch that is formed using alpha-glucose units. The beta acetal linkage between units allows for linear chains hence branches are unlikely. The alpha acetal linkages allow for spiral chains. The beta glucose is good for structural polysaccharides because it allow for best interaction between polymer chains and increases the integrity and strength of the cells wall.