wages and labor costs reflect the value of the marginal product of labor, not the general or average "productivity" of labor.
If you over-educate a population, that shifts the supply curve of skilled labor to the right, which brings down wages, while also increasing unemployment. It's similar to drilling for oil causing a surplus of oil or driving the price down. With too many people going to college, the value of a degree decreases
It's true the lower wage rate will cause more educated labor to be hired by the firm. The firm takes advantage of the government aid to education, training their employees for "free," Michelle Obama is wealthy, but even she complains about her huge debt she had from loans for college. The government aid drives up the cost of education and makes the college degree less valuable, leaving the students with back breaking debt. The winners? Those companies that get to hire more and cheaper skilled workers. The consumer also benefits from cheaper labor reflected in less expensive products.
