When college rankings are a stain on society for encouraging colleges to do all the wrong things in order to improve their standings (new sushi bars, $5M football coaches, fudging acceptance data, etc), we shouldn't even be entertaining the idea of ranking high schools.
If products costing $10-$100 are ranked on Amazon and elsewhere, it is inevitable that people consult rankings on purchases of $200K+.
One reason college rankings are based on some unimportant criteria is that colleges, especially the most prestigious ones, do not want to publish data on learning outcomes that would let them be compared. Do Harvard students learn more in their 4 years than comparably bright students going to state schools? Since the answer may be "no", it's not in Harvard's interest to coordinate with other schools to create the data that could answer this question.
