I see very plainly how the parent theme is registering the widget area (in parent theme's functions.php file):
add_action( 'widgets_init', 'theme_widgets_init' );
function theme_widgets_init(){
register_sidebar( array (
'name' => __( 'Sidebar Widget Area', 'text-domain' ),
'id' => 'primary-widget-area',
'before_widget' => '<li id="%1$s" class="widget-container %2$s">',
'after_widget' => "</li>",
'before_title' => '<h3 class="widget-title">',
'after_title' => '</h3>',
) );
}
In simple theory, I don't know why this code (in the child theme folder's functions.php file) is not killing the sidebar widget area from displaying in the backend in Appearance > Widgets:
add_action( 'widgets_init', 'unregister_parent_sidebar' );
function unregister_parent_sidebar(){
unregister_sidebar( 'primary-widget-area' );
}