There's something wrong with a system where a person has absolutely no options for travel in certain circumstances.
A less regulated market would quickly fill the void by starting up a "premium" taxi service for a premium price. Maybe charge double the fare, but provide a service and availability guarantee?
There are enough affluent people out there getting drunk who would happily pay twice the price (or more) for this kind of service. Or would this start a slipperly slope towards two-tier health care?