Field groups that contain only elements that use #markup are hidden

Most form elements have a #type set. In fact, all valid form elements except one kind have that.
This is in drupal_render():

  // If #markup is set, ensure #type is set. This allows to specify just #markup
  // on an element without setting #type.
  if (isset($elements['#markup']) && !isset($elements['#type'])) {
    $elements['#type'] = 'markup';
  }

However, field_group_remove_empty_form_groups() ignores this distinction, and removes anything without a #type.

Additionally, it loops unnecessarily. Once it finds one child, it can stop looping.