Force all child pages to use template?

Is there a way to set all child themes of a specific parent to use a specific template? I found this code but it doesn’t work out of the box with Sage due to the base.php. Is there another way around it?

 * Automatically apply parent page template
 * Inspired by:
function fstop_use_parent_page_template() {
// Checks if current post type is a page, rather than a post
if ( is_page() ){
	$ancestors = get_post_ancestors( get_the_id() );

	if ( $ancestors ) {
		$parent_page_template = get_post_meta( end( $ancestors ), '_wp_page_template', true );
		$template = TEMPLATEPATH . "/{$parent_page_template}";
		$current_page_template = get_post_meta( get_the_id(),'_wp_page_template', true );

		if ( file_exists( $template ) ) {
			load_template( $template );
			update_post_meta( get_the_id(), '_wp_page_template', $parent_page_template, $current_page_template );
	} else {
		return true;
add_action( 'template_redirect', 'fstop_use_parent_page_template' );

Setting a page template should work regardless of base.php. WordPress doesn’t really know or care about base.php.

What effect are you seeing? In what way is this not working? When you ask a page what its template is after using this method what happens?