The reason why education works is that it makes all parts of society function better. Having an educated population produces a higher functioning society. That's a society that, more often than not, is able to produce more wealth faster. In fact, it's in the enlightened self interest of society to have a broadly educated population. Basic research winds up driving GDP growth as science goes from the lab to products. Having more engineers and scientists is important, but so is having musicians, writers, nurses, and so on. All these types of education are important in a modern society. What's going on in the United States is that we are slowly short changing ourselves by making it harder and harder for people to get that additional education.
But in the process we're also creating a more stratified society. A lot of social mobility comes from the "first generation to go to college." By making college education less affordable, we keep people in the lower and lower middle classes that could have a transition up the income ladder from lower skilled, lower paying jobs to white collar professions. That's just one way we're becoming a society with little social mobility. American has moved away from the meritocratic American ideal. Now, even if you're an idiot, if you start out rich you'll probably stay rich. If you're poor, even if you're smart and capable, you'll probably stay poor.