With all due respect, that's not right. Any student attending a prep school from kindergarten, or otherwise very early, will have their development accelerated as compared to a child who attends an average school. The effect compounds with each year.

This doesn't somewhat improve college performance. It creates a markedly different brain and habits. An effect that declines as entrance into such a school system becomes later. Middle school being exceptionally late. High school being so late so as to have a marginal effect if any. Kindergarten being optimal.

Prep schools, generally speaking, only give basic test instruction for college entrance exams. Other standardized testing is the same or even less than normal schools. Cram-course style instruction is generally private and paid for privately by any given family. In my experience, the vast majority of prep school students don't seek it. This is in the United States.