FAFSA's influence doesn't begin and end with the government. Many colleges also use the form as a way to streamline the information needed for their financial aid process. Like the government, many colleges also take savings into consideration.
From a pure logic standpoint, this makes sense: if a family has savings with which it can pay for college tuition and related expenses, then it should. But this logic has a clear flaw -- saving doesn't get there by accident; it is a behavior that you generally have some control over. Unless a family has very high income, it can always spend its income on something else instead of saving if it chooses. And those very high-income families wouldn't qualify for aid anyway.
So by considering savings, the government and universities discriminate against families who make the choice to save. They provide greater aid to a student whose parents have not accumulated as much money over the years.
Let's make this example concrete. The FAFSA website has an aid estimator that I played around with a little. If you have two students applying for aid whose family has precisely the same characteristics, then saving impacts how big of a Federal Pell Grant they will qualify for. In the scenario I created,* the student in a family with zero savings would be awarded a $4,000 annual grant. If that family had $50,000 in the bank the student would only qualify for $3,800. If that savings is $100,000, then the grant drops to $2,400.
This isn't a huge variation, but federal financial aid is pretty minimal to begin with. A more substantial portion is often awarded by the colleges themselves. And they also often consider savings as a key metric in their aid decision. For example, Georgetown University's financial aid website says (my emphasis):
Your eligibility for Georgetown University scholarship assistance is determined using a need-analysis formula, similar to the federal model, but which analyzes additional factors Georgetown believes affects students' ability to contribute to educational expenses. In order for limited funds to be shared most equitably, the university expects that each student and his or her family will contribute to the fullest extent possible to meet educational expenses and will draw on income and all family net assets (including home equity).
Is This Really Unfair?
Some reading this might think: "But wait -- don't families with higher incomes generally save more money?" Yes, they do. But if you're worried about income, then you can judge a student's ability to pay by using that criterion. You could even ask parents for a 10-year income history.
This would be fundamentally different from considering saving as well. Unless a family is living very near the poverty line, it can choose to save something. Doing so just takes sacrifice. They can live a little further out of town so that their housing expense is cheaper. They can clip more coupons -- a few dollars here and there add up over a year's time. But to a college admissions office, that sacrifice merely results in their looking better able to pay than parents with the same income that chose to spend more money instead.