How does an incentive to work accomplish anything if the only jobs that are available (if any for a given person's skillset) are ones that pay far too little to live on. ("decreasing the cost of labor" == "reduce or eliminate the minimum wage")
Most poor people work very hard to earn enough to survive; much harder per $ earned than most people on this website. They don't need an incentive to work, they need jobs that pay better for each hour they work.
Raising the minimum wage won't accomplish that by itself, because most companies would reduce the number of positions to keep their costs stable. We could raise the minimum wage and then provide tax credits to businesses to offset the additional labor cost, but that'd wind up complex to administer and there would probably be loopholes that allow companies to take tax credits and keep the cash to themselves instead of paying them through to employees. With Basic Income, we effectively raise the minimum wage by direct payments to the employee; their income per hour worked goes up. This is much simpler to administer: everyone gets the same amount, and it counts as taxable income.