If you look at the voting statistics, majority of uneducated and lightly educated (high school only) votes Democrat. College graduates lean Republican, while higher degrees (academia) leans Democrat. So it would be counterproductive for Republicans to have more less-educated voters, since those prefer Democrats.

Education spending is another red herring - public schools spend no less and sometimes more than private schools, costs of K12 education per pupil tripled since 70s with little to no improvement in any measurable metrics, teacher employment has grown faster than enrollment for 40 years now. http://www.cato-at-liberty.org/president-we-need-more-teache...

Sorry for ruining your nice theory with facts.