 If a HV theory satisfying these conditions were feasible, we would have a natural explanation of the statistical character of QM, and an elegant way of resolving the infamous measurement problem haunting all interpreters of QM (see the entry on  quantum mechanics  and the section on the measurement problem in the entry on  philosophical issues in quantum theory  for details). What the KS theorem shows is that a HV theory of the most  straightforward sort, satisfying these conditions, is not an option.   The HV program is left with  only options that violate one or more of  these conditions; see entries on  Bohmian mechanics and  modal interpretations of quantum mechanics.