One basic problem of our economy is that unskilled labor is perfectly competitive, meaning that the price of unskilled labor is always driven down to the cost of subsistence. Combined with high structural unemployment, this also means that bosses can treat workers ever worse, because the workers have ever fewer options. As technology improves faster, automation becomes more frequent and things look even worse for the unskilled laborer because there are not even enough unskilled jobs to go around. We have historically solved this problem by making it more attractive to hire unskilled laborers rather than replace them with automation, but this has a trade-off: it retards technological progress, and we end up with a bunch of people doing terrible jobs that could easily be replaced by robots, just because we have a moral preference for work. We could, however, give an incentive to innovation and automation while also avoiding the problems of mass poverty. If everyone received a basic income just sufficient for subsistence, then workers could quit their terrible jobs without starving, and a large portion of these jobs could be automated without leading to any social crisis. We could also do away with restrictions on the labor market that make it difficult to hire and fire unskilled workers (such as the minimum wage), because losing your job would not put you in danger of starvation. Technology could finally spring ahead unimpeded by politicians distorting the labor market in order to save obsolete jobs. There would be large efficiency gains in society as a whole, as we could eliminate complex welfare schemes, and probably a lot of employment litigation as well. It is not a perfect system, since much of the gains would be redistributed from the owners of capital (who will benefit from the automation) to our unskilled laborers. This is, of course, a massive distortion in the labor market, but I would argue that it is a better distortion than the complex system we have now, which hinders technological progress. Instead of forcing companies to keep people in obsolete jobs, these workers would have time and opportunity for re-training, increasing the pool of skilled laborers and making technological investment easier. If someone is really unable to learn any useful skills, they might just receive the basic income and remain unemployed, but this is already what happens in our current economy; we just have a gigantic welfare bureaucracy designed to pretend that we're not already doing this. A basic income would streamline welfare and shrink all levels of government massively, leading to further savings.
You might say that it's immoral to give millions of people a living wage for nothing, and that it will ruin the country, but we actually already do this: it's called "inherited wealth." Many millions of Americans inherit enough wealth that they would never have to work if they didn't want to, and yet they are still in the labor force. Humans have worked for millions of years. Each generation has left something lasting for the following generations to build upon, and we're finally reaching a point whereby we can successfully automate most unskilled labor. By instituting a basic income, we would simply acknowledge that the world's capital stock is, to a certain extent, the common heritage of mankind. We would also get a lot of awesome robots.
Actually, maybe I'm totally wrong and a basic income combined with eliminating a minimum wage would make it more attractive to hire humans, since you could pay them less. Who knows? What's the worst that could happen?