Those guys are few and far between. Most players like that:
A) Would rather continue to PLAY basketball (like skb said), so they go to a D-3 type school. Many times those schools help out with academic scholarships.
B) Are tired of working their tails off throughout high school and are ready to get to college and not be tied down to an every-day training regimen. A.k.a. they leave their "high school hero" status behind and move on with life after sports.
C) Desire to play at the D-1 level but have no discipline to truly do so. On top of a variety of other factors, this lack of discipline plays out in the student's GPA. We know that if we are going to have walk-ons, they need to be GPA-boosters for most of our scholly guys.
That is not an exhaustive list, but that really narrows down the playing field. When you're spending hours upon hours on a daily basis being the scout team dummy without the incentives of a full scholarship, few college kids have the ability, desire, and discipline all in one. It's just how it is.