Task Template inheritance option

Would be great if there was a way in a Task Template to specify fields that should inherit the value of a similar field on the parent entity it the template is assigned to.  For instance, we have a Scene link field on Tasks that we would like to always have the same value as the Scene link field on its parent Shot.  (Necessary to allow viewing of Scene-based columns on Task grid pages.)  Could also be useful for Due Dates, or if you want the Task Type to mirror the Shot Type of the parent.