Load child template based on parent

Instead of putting something on the template, you can keep templates clean and add to functions.php a function that use 'template_include' action hook to check parent page template and return same template for children pages.

add_action('template_include', 'auto_child_template');

function auto_child_template( $template="" ) {
  if ( ! is_page() ) {
    return $template;
  } else {
    $page = get_queried_object();
    $ancestors = get_post_ancestors( $post );
    $templates = array();
    // add ancestors page templates to $templates array
    foreach ( $ancestors as $ancestor ) {
      $templates[] = get_page_template_slug( $ancestor );
    }
    // remove empty values
    $templates = array_filter($templates);
    // if no ancestors has a template return current one
    if ( empty($templates) ) return $template;
    // fallback
    $templates[] = 'page.php';
    return locate_template( $templates, FALSE );
  }
}