How can a report be designed so that any changes to a user's user POV changes the members selected from a row, column, or page axis on a grid?

Use the CurrentPOV member for the selected axis or choose a member selection function with CurrentPOV as the member parameter. When the report runs, the axis value is taken from the user POV. You can design a grid so that all axis values are taken from the user POV, making the report completely dynamic on a per user basis.