Complete disruption of cell walls and plasma membranes of cells and organelles is absolutely required to release all RNA contained in a sample. Different samples require different methods to achieve complete disruption. Please refer to the section 'Disruption and homogenization of starting materials' in the RNeasy Mini Handbook. Incomplete disruption results in significantly reduced RNA yields.
Homogenization is necessary to reduce the viscosity of the cell lysates produced by disruption. Homogenization shears the high-molecular-weight genomic DNA and other high-molecular-weight cellular components to create a homogeneous lysate. Incomplete homogenization results in genomic DNA contamination, and inefficient binding of RNA to the RNeasy membrane resulting in reduced yields.