Apple TV Plus, CBS All Access Showtime Bundle, NO access to Late Show
Are you able to watch the Late Show on CBS All Access Showtime Bundle (now Paramount +) ?
Sometimes it works the next morning, sometimes it is the next day, sometimes it never allows access. When it does not allow access, the system wants you to sign in to Paramount + which is a totally separate way of getting the content. Obviously you cannot use your Apple credentials for this although Apple support is not totally clear on this point, at least on one occasion.