No reliable method exists for clearing the Twig cache

The current method of clearing the twig cache (as seen in drupal_flush_all_caches) is this:

  // Wipe the Twig PHP Storage cache.
  PhpStorageFactory::get('twig')->deleteAll();

That clears the local directory that stores the twig cache.

Unfortunately, there is no guarantee that that directory is shared across web servers. The expectation for anything in drupal_flush_all_caches is that it actually flushes/invalidates across the entire site, which the twig case violates.