And the Expected Family Contribution can blow your mind how large it is. Especially for middle class folks like me who had a child go to school at a State University. I don't recall what the tuition was as she graduated 6 years ago, but currently it is $7,400 and my EFC was several times that amount. But FAFSA does open the door to loans and other financial assistance that is not tied to income
Your second statement depends on the college. My youngest's college has two types of aid - need based, which requires a FAFSA, and merit, which does not. We haven't bothered filling out the FAFSA since her applications (we filled it out then because some schools she was applying to required it as part of the application - you could come from a family of tech billionaires and they'd still want a FAFSA - although I suspect a building sized donation might waive the requirement for paperwork).
EFCs ARE high. The government starts with the assumption that its taken you eighteen years to raise this kid with the awareness college is coming and that you saved something - they then take your current income to figure out how much you should have been saving for the past few decades - this can make it really difficult if your income jumped significantly just as your kids hit high school. They do this without much regard for your expenses during those eighteen years. Moreover, middle class parents should be prepared that the aid package offered by the federal government will consistent mostly of LOANS - federal grants have low qualification thresholds. Plus, perhaps work study. Parents should also know that being qualified for work study jobs on a FAFSA does not mean a job will be available to your kid at college. At my youngest's school, getting a work study job is competitive and a lot of students never make any work study money. Individual colleges may stack more money - needs based or merit based, on top of the federal money. And while its possible to go back to a school and ask for more, it doesn't always work. I know of one school where I've heard a lot of parents/students say "that was our first choice, but they wouldn't budge on the financial package."
The last thing to be aware of is that merit scholarships will often require a student to maintain a GPA. Watch what that requirement is. Keeping a 2.67 your first year is way easier than keeping a 3.25. And college, and being away from home, getting ill, facing hundreds of pages of reading or papers with high expectations, and your great student can find that 3.25 is hard to keep.
You can find FAFSA estimators online which will give you an idea of how much to even sweat this. If your income is high or you saved a bunch of money, it isn't going to make any difference.
(I'd hang onto the cash, it will count against you for FAFSA, but since you will be qualifying for subsidized loans (most likely) under FAFSA (if you aren't like tvguy or me and find that you qualify for nothing at all - we 'helpfully' got a suggestion to use a private bank for a private parental loan) its really a matter of "do you want a bigger mortgage loan or student loans." One way or the other, you'll need the tuition in hand to pay the bill. My mortgage has a low rate and I write it off on my taxes and its mine, not my students. But my attitude is part of my parental responsibility is to pay for college - the kids having student loans would be a last resort for us.).