Inevitably, increasing the demand for a given product or service will also increase the price associated with it. So we did in fact increase the amount of people in the country who are pursuing higher education, but at the cost of increased tuition, extra fees, and expensive textbooks.
To deal with the increased price, policy-makers decided to up the amount of federal aid offered. Of course, since (for the most part) everyone who wants to go to college is going at this point, this doesn't increase demand by adding any new people to the market. Instead, we just increase the amount that schools can charge students before those students will get fed up and leave.
So of course student loans are going to be a problem. The very act of providing them means schools can jack up the price, which means students need more money. Since nobody likes the thought of denying someone access to education, more loans are offered, which raises the price even more. Ironically, the real effect of these loans is that it takes a great deal of money to college without being financially crippled for life, which hurts the poorest in our society more than anybody.