A situation in which assistance is given to people who are working (albeit for a lower wage) is a much better situation than assistance being given to people who aren't working at all.
There is value in enabling people to have jobs, even low paying jobs.
Many workplace laws and regulations effectively increase the cost of labor in the aggregate. So "decreasing the cost of labor" is not all about lowering pay. Think of things like overtime rules, mandatory benefits, onerous compliance rules, shifting various legal burdens to the employer rather than the employee, making it more difficult to fire someone.
How many people with 3 kids do you think are going to stop working if they get an unconditional government benefit of $6,000?
I think the EIC does a good job of addressing the need some people have to moralize about the sanctity of labor, I doubt it has much of any impact on the labor market (it mostly just makes the lives of some kids better).
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.