Lots of great schools outside of the Ivy's. Besides, private school alone doesn't guarantee Ivy admission. That angle has actually gotten much more difficult in recent years. Today, it might actually be better to be a standout student and a good athlete in a public school if you want Ivy.
Back to the point, "wealthy parents" paying for private school or a PG year aren't doing it for a scholarship. It's for the chance to get their kid a D1 slot. As for Ivy, which by the way don't offer athletic scholarships, if that's the motivation for a PG, then you need to know where your kid stands with a target institution before going through the effort.
