Even with open borders and a global economy I think UBI is inevitable; the real question is whether we get there through carefully crafted laws and human compassion, or whether we get there kicking and screaming through half-measures and bureaucratic red tape.
Throughout history there was always a way to use additional labor productively (more farmers more factory workers more whatever), so we based our method of divvying up our resources by how much you contributed. Well with robots and drones, and self driving vehicles, and computers taking over jobs that used to need to be done by humans that system won't work. When there's only 50 jobs for every 100 people who need to make a living, something's going to have to give. We've already decided that we're generally not ok with the idea of our populace starving or being homeless, so we need to implement some sort of welfare system, the question really is what form it will ultimately take.