Scholarships have a dramatic influence on which school an athlete chooses to attend but scholarships are very over rated. Unless a athlete is getting a full ride the most important number is the balance the athlete will be straddled with. Many schools talk about their great academic aid and forget to mention that the kids will still have to pay $X0,000/year.
My completely unsolicited advice for any high school athlete is to remember that the college system went through the recession as well. Furthermore, don't let a scholarship determine where you go to school. Most schools break up scholarships to help the entire team meaning that most kids are getting a small percentage of their education covered.
The reason why people are dead set on earning a scholarship has more to do with the parents wanting to brag to their friends than the actual financial benefit. For any dissenters think of the return on investment. The amount of time and money spent by families traveling to meets, equipment, gym membership, rehabilitation, PT and coaching can be staggering. I know that our sport is not the best example but look at soccer and fact that you HAVE to play club soccer ($3K+/season) to get a scholarship. We are becoming professionalized at younger age every year and the cost to be at the top will continue to grow.
It is nice to get a scholarship but it is far better to run for a school where you are happy and can develop. I've seen my fair share of sub-4:15 milers go to crappy schools chasing money; very few have gotten faster.