Some places in Indy do this, but it has nothing to do with being cheap, per my DH who has been working in the restaurant industry for almost 20 years.
If employee A stays after work and is being served by employee B, there's a good chance that there will be chatting and socializing. That leaves other customers unattended, and looks bad for the establishment.
TGI Fridays does this, or at least they used to. Before they put the policy in place, employees would come in on their days off or after shift, take up a large portion of the restaurant, get a discount on their food, get drinks not made to company standards, and generally be obnoxious.
Plus, in a lot of states, if a restaurant serves you too much alcohol and you drive drunk and get into an accident, the restaurant, manager, bartender and server can all be held liable.