Another thing is that usually the "automatic gratuity" is not entirely given to the wait/service staff. The house keeps a large portion of it, and expects that the diners will tip the staff separately.
False. It is in fact illegal for the business to accept any income designated gratuity as revenue. Servers may be required to tip out other employees with tip-based wages, i.e. bartenders/bussers, but it has to be on established and consistent percentage based scale.