The cost-per-student of private vs public education is not an apples-to-apples comparison because the public school system is also obligated to provide transportation and special needs education, both of which are very expensive and neither of which are in scope for most private schools.

The EU and Canada have those costs too... and are still spending way less per student than the US.

Indeed, and it'd be worthwhile doing a comparison. My only point is that you have to make sure comparisons are accurate with respect to scope of services.

Private schools in the US look artificially good in terms of both finances and performance because they end up selecting the more privileged students to start with.