Standardized test scores that the rich kid's parents can throw away thousands to specifically train their kid's to take both in their cozy private school atmospheres and special courses... Only to have their over achieving test taking child fail out of college because they don't have the intellectual capability to form independent thought or write a coherent term paper. Unless those private colleges are more interested in the tuition than academic integrity which I am sure also happens... Standardize tests scores are a gauge for potential ability, and nothing more.
From a public school perspective, having different levels of requirements are going to change the incentive of how much a particular student will study for the test. For example in Iowa, as long as you are top 50% on the test and in your class, you can get into UI/ISU/UNI. Why would someone expend so much energy and time when they know they can get in, as opposed to a kid who wants to go to UNC/UCLA/Larger state public school. I get the scholarship thing, but you have to remember that seems like a decade away for 16 year old kids taking the exam...
Just my .02