The correct course of action is to call a cab for the customer who is too drunk to drive themselves home. This ensures their safety and the safety of others on the road. Offering a cab provides a responsible solution to prevent potential harm or legal consequences that can arise from drunk driving. It also demonstrates a high standard of care and responsibility on the part of the bartender, as ensuring patrons leave safely is a crucial aspect of alcohol service.
Letting the customer stay until they sober up might not be the most responsible choice, as it could lead to further intoxication or prolonged exposure to unsafe situations. Suggesting that they walk home could also be dangerous, especially if the customer is severely impaired, as they may encounter hazards or get lost. Offering another drink counteracts the goal of ensuring the customer's safe departure and can greatly increase the likelihood of further intoxication, leading to unsafe choices. Therefore, arranging for alternative transportation, such as a cab, is the most appropriate and responsible option in this scenario.