Why is the Last-Modified header not being returned?

Question

Computer networks

I need to add the title specified in the title, but it does not work. Here is the code I am using:

function add_header_xua($headers) {

  if( is_singular() ) {
        $post_id = get_queried_object_id();
        if( $post_id ) {
            $headers['Last-Modified'] = get_the_modified_time("D, d M Y H:i:s", $post_id);    // не появляется в заголовках
            $headers['Last-Modified2'] = get_the_modified_time("D, d M Y H:i:s", $post_id);  // появляется в заголовках  
        }
    }

    return $headers;     
}
add_filter('wp_headers', 'add_header_xua');

Answer 1

Understood and set up.
1) Changed PHP version from 5.4to 5.6
2) Changed filter wp_headersto action template_redirect. Since at the time wp_headers is triggered, the $post type variables have not yet been initialized, which means that all post type checks, getting its ID, etc. - impossible

function lastmode_headers() {

  if(is_singular()) {
    global $post;
    $LastModified = get_the_modified_time("D, d M Y H:i:s", $post->id);

    $IfModifiedSince = false;
    if (isset($_ENV['HTTP_IF_MODIFIED_SINCE']))
      $IfModifiedSince = strtotime(substr($_ENV['HTTP_IF_MODIFIED_SINCE'], 5));  
    if (isset($_SERVER['HTTP_IF_MODIFIED_SINCE']))
      $IfModifiedSince = strtotime(substr($_SERVER['HTTP_IF_MODIFIED_SINCE'], 5));
    if ($IfModifiedSince && $IfModifiedSince >= $LastModified_unix) {
      header($_SERVER['SERVER_PROTOCOL'] . ' 304 Not Modified');
      exit;
    }
    header('Last-Modified: '. $LastModified);  
  }
}
add_action('template_redirect', 'lastmode_headers');