To quote Dave Barry, from 1982 but still relevant:

"Now the problem poor people have is obvious: they don't have enough money. They can't afford food, housing, or medical care. The simple, obvious, efficient way for the government to help them is to give them money so they can buy these things. So that is not how the government does it."

This is basically the libertarian argument for a basic income: if we're going to have an expensive welfare state, it should be efficient and it should actually accomplish its stated goals.

poverty is often directly correlated with the level of education.

It's even more directly correlated with the level of money.

Poverty is correlated with education because education is expensive. If the causation doesn't go in the direction you expect, solving poverty with free college might be like solving poverty with free yachts and free diamonds.