I'm not sure the quality of the private schools you mentioned (O'Dea or Bishop Blanchet) are on par with what others consider as elite private schools. For one,

I'm not sure the quality of the private schools you mentioned (O'Dea or Bishop Blanchet) are on par with what others consider as elite private schools. For one, those two schools have tuitions in the 10k-15k/yr range which is pretty low. Private schools in the northeast, like Milton Academy or Phillips Exeter are in the 45-50k/yr range. These schools also tend to have higher than average matriculation rates to elite universities like the Ivies as well. Teachers at those schools are definitely making more than their public school counterparts.