It's not what people typically did because taxis were not generally available in most US cities. You couldn't rely on a taxi coming to pick you up at your home nor rely on one being there when you wanted to leave.
Nevertheless there are other options, such as calling a friend, taking the bus, walking, etc. It's not clear that Uber resulted in people who would otherwise have been drunk drivers instead calling a cab. People who drunk drive presumably don't arrive at that choice because of a minor inconvenience.
