Core activity forms, pages / selectors should be integrated with the new Case/Activity codebase so that Case_Activity extends Activity_Activity classes.
Case-related activities should NOT be displayed on the CiviCRM (home) dashboard, and also NOT displayed on the Contacts' Activities tab. We can add a parameter defined by each component which indicates whether that component's activities are included in the "core" activities listings (dashboard and tab). Default is true. (i.e. showActivitiesInCore). CiviCase would set this to false.
NOTE: Let's maintain the conditionally displayed "Case" comboBox field which appears on new / edit Activity form when Cases are enabled. However, this should only be included on the form when the target contact "has" one or more cases to be displayed in the comboBox. It should also be suppressed in "standalone" mode (e.g. New Activity from shortcut block).